
Class ._ 

Book _^ . ^^ 

Copyright iN!' 

COPYRIGHT DEPOSIT. 



ELEMENTS OF PHYSICS 



7h§?)<^>^ 



■s 9 "^ "* o 



ELEMENTS OF PHYSICS 



BY 



ERNEST J. ANDREWS 

INSTRUCTOR IN SCIENCE IN THE ROBERT A. WALLER HIGH SCHOOL 
CHICAGO, ILLINOIS 



H. N. ROWLAND 



INSTRUCTOR IN PHYSICS IN THE SOUTH DIVISION HIGH SCHOOL 
CHICAGO, ILLINOIS 



TO WHICH IS ADDED 
A MANUAL OF EXPERIMENTS 



N£h3 gork 
THE MACMILLAN COMPANY 

LONDON : MACMILLAN & CO., Ltd. 
1903 

All rights reserved 



THE LIBRARY OF 
CONGRESS, 

Two Copies Received 

FEB 20 1903 

, Copyright Entry 

CLASS (X^ XXc. No, 

COPY B. 



Copyright, 1903, 
By the MACMILLAN COMPANY. 



Set up and electrotyped January, 1903. 



Norhjooli i^rcsg 

J. S. Cushing & Co. — Berwick & Smitl\ 
Norwood Mtiss, U.S.A. 



PREFACE 

A FEW words in reference to the plan of this book may 
assist those interested. 

1. In earlier days, when laboratories were little used, 
much more time was spent on physics in the classroom 
than now, and more ground could be covered, though 
with far less profit ; while in recent years development 
of the science has added much to the subject which neces- 
sarily enters into its elementary study. As a consequence, 
the field laid out by the earlier writers was broader in 
some directions and narrower in others than is now war- 
ranted. Peck's Ganot, for instance, devoted fifty-four 
pages to statical electricity and forty-one to the remainder 
of the subject. 

Much has been done by recent writers to secure proper 
limits ; it can scarcely be said that the newer develop- 
ments have been slighted, and the old field has been 
narrowed. But we feel that the ground ordinarily cov- 
ered is still somewhat broader than one year of study 
warrants ; and have here narrowed it slightly in accord- 
ance with the general plan stated below. 

2. Again, the old classroom method usually produced 
only vague notions. But the method was thought valua- 
ble, and the impression exists now that our much more 
scientific method must of necessity produce valuable re- 
sults. Yet the conceptions formed by many, even of the 
better students to-day, are often vague and incorrect, and 
the poorer pupils frequently miss the point altogether. 

We have thought this to be due partly to the use, in 
text-books, of language not clearly understood by the 



VI PBEFACE 

student; partly to the failure of tlie author to discrimi- 
nate in his explanations between tlie easy and the difficult 
subjects ; and partly, we fear, to his own misconceptions. 
At any rate, we have given special attention to those sub- 
jects which experience has shown to be particularly diffi- 
cult for the students ; and have attempted first to view 
them correctly ourselves in all their bearings on physics, 
and then to express them as fully as their abstruseness 
demands and in such terms as appeal most strongly to the 
understanding of the average student. Unfamiliar terms, 
which are necessary to the study, we have introduced with 
less difficult subjects. 

3. We have sought to make prominent the practical 
bearings of physics. 

To those students at least whose schooling ends with 
the high school, physics should be a connecting link be- 
tween their study and their work. Except in special cases 
it bears more on the daily affairs of life than any other 
subject, and thus gives an opportunity of emphasizing the 
practical value of study. This we have attempted to do ; 
and have also sought to connect high-school mathematics 
with practical life by breaking away from formulas and 
set equations, and obliging the student to carve out his 
own processes, as is necessary in most applications. 

We have also followed the plan adopted by some of in- 
troducing bits of history, in order, partly, to show the close 
relation between the science of physics and human life. 

4. Finally, we have based the work on a few funda- 
mental principles, seeking first to clearly express these 
principles, and then to refer back to them phenomena sub- 
sequently considered, so as to form, from beginning to 
end, a series of closely associated subjects. This we have 
done in the belief that a science can be studied success- 
fully only when so presented that the relation of each 



PBEFACE Vll 

phenomenon or fact to others and to the science itself is 
clearly recognized, and that when so presented physics, 
as a means of mental development, is inferior to no other 
subject. 

5. The general plan, then, has been to eliminate a few 
subjects which have no practical bearing, and the relations 
of which to the fundamentals cannot well be made ap- 
parent; to present difficult subjects fully and in simple 
terms ; and to connect each subject, directly or indirectly, 
with every other by fundamental principles or their 
corollaries. 

6. In doing this we have depended partly upon our own 
experience in the classroom and the laboratory, and partly 
upon the experience of others, seeking to base each step 
on a sufficient demonstration of its worth. And we wish 
here to extend our sincere thanks to those who have 
assisted us in this way and in the more laborious work 
of issuing the book. 

We are fully aware that our efforts have not been in 
all respects successful. We trust, however, that some- 
thing has been done to assist in giving physics the promi- 
nence in secondary education which it merits ; and our 
hope is to continue the work by a revision in the course 
of a few years, making such changes as experience and 
the development of the science may dictate. To assist in 
this we shall be grateful for any suggestions or criticisms 
from others ; and to make such criticisms directive, it 
may be well to state that Mr. Andrews is primarily re- 
sponsible for the Introduction, Chapters II, III, VI, VIII, 
and IX, and Mr. Howland for Chapters I, IV, V, and VII. 

E. J. ANDREWS. 

H. N. HOWLAND. 
Chicago, 

December, 1902. 



CONTENTS 



Introduction 



PAGE 
1 



SECTION 

1. Structure of Matter 

2. Properties of Matter 



CHAPTER I 
Matter 



6 
13 



CHAPTER II 
Motion and Force 

1. Motion 21 

2. Force 26 

3. Laws of Motion and Force . 28 

4. Units 36 



CHAPTER III 
Gravitation 

1. Universal Gravitation 45 

2. Gravity 51 

3. Falling Bodies 56 

4. The Pendulum 63 

ix 



X CONTENTS 

CHAPTER IV 
Mechanics of Solids 

SECTION PAGE 

1. Energy and Work 74 

2. Machines 82 

3. Friction . . . .92 

CHAPTER V 

Mechanics of Fluids 

1. Hydrostatics 98 

2. Buoyancy 106 

3. Specific Gravity 108 

4. Mechanics of Gases 112 

CHAPTER VI 
Heat 

1. Causes, Sources, and Nature of Heat 125 

2. Efeects of Heat 129 

3. Transference of Heat 143 

4. Heat Measurements 150 

5. Heat and Work 162 

CHAPTER VII 
Electricity 

1. INIagnetism 177 

2. Static Electricity 184 

3. Voltaic Electricity 197 

4. Electric Currents 204 

5. Effects of Electric Current 214 

6. Electrical Measurements 222 



CONTENTS XI 

SECTION PAGE 

7. Electromagnetisra 237 

8. Induced Currents . . . 243 

9. Practical Uses of Current Electricity 257 

CHAPTER YIII 

Sound 

1. Cause of Sound 274 

2. Propagation of Sound 276 

3. Variations in Sounds 283 

4. Sound Vibrations 290 

5. Reception of Sound-waves 299 

6. Music 303 

CHAPTER IX 
Light 

1. Nature of Light 308 

2. Propagation and Transmission of Light .... 310 

3. Reflection of Light .317 

4. Refraction of Light .331 

5. Applications of Refraction ; 340 

6. Chromatics . 349 

Appendix 369 

Index 377 



ELEMENTS OF PHYSICS 



INTRODUCTION 

In taking up the study of physics the student should 
first form a clear conception of its scope. He should 
know what subjects are to be treated and the general 
method of their treatment. In order to assist in this we 
will discuss briefly the meaning of science generally, the 
branch of science called physics, methods of treating sci- 
entific subjects, and methods of studying physics. 

1. Science. — Early in life the child learns that a dish 
shoved from the table will fall to the floor ; that if it 
strikes his foot it will hurt. He also learns that a spoon 
falling to the floor will not break, while a tumbler may ; 
that a napkin falling on his foot will not hurt. And 
many facts of a like nature are soon learned. 

These are independent facts, apparently unconnected 
with each other. Knowledge of such facts is simply 
general knowledge. 

But as the child grows older he begins to connect simi- 
lar facts. He concludes that all bodies left unsupported 
will fall ; that any heavy body falling on his foot will 
hurt, while light ones will not; that few metal dishes 
break when dropped, while most glass dishes do. Facts 
are thus collected by him and classified; his knowledge 
becomes systemized, — it becomes scientific. Scientific 



2 INTRODUCTION 

knowledge, then, is merely general knowledge classilied. 
And science is the knowledge of such relations among 
certain facts or truths as may be gathered in groups or 
classes. 

2. Physics. — Facts which may be classified, referring 
to plants, flowers, and the like, give us the science of 
botany. Such facts referring to the planets, stars, and 
the like give us the science of astronomy. So to under- 
stand what is meant by the science of physics we must 
know what facts are implied by the word physics. 

Comparing the different objects around us, we find that 
stone is hard, rubber is soft ; wood is solid, water liquid ; 
objects differ in color, in weight ; some are warmer than 
others ; some are in motion, others at rest ; some move 
faster than others ; some are used to conduct electricity, 
others are not. Objects evidently differ from each other 
in many respects. On the other hand, some resemble 
each other in many respects, while they may differ in 
other respects. The objects we see around us, then, may 
be alike or unlike, and it is these likenesses and unlike- 
nesses between objects that constitute a portion of the 
science of physics. 

At the same time a close^ study of the subject shows 
various causes for these peculiarities of objects ; shows us 
many laws which govern the appearance and condition of 
objects, — why some bodies are hot, some cold, some light, 
others dark ; what causes the locomotive to run and the 
telephone to speak. These causes, or the laws according 
to which differences are brought about between various 
objects, constitute the other portion of physics. 

Physics, then, is that branch of science which refers to 
tlie differences between objects, to the various phenomena 
by which our senses are affected, and to the laws causing 
these differences and phenomena. 



INTRODUCTION 3 

3. Scientific Methods. — In the treatment of any scien- 
tific subject the author usually has in view one of two 
purposes. He desires either to give simply facts and 
laws bearing on the science, or to impart to the reader 
or student scientific power. Many scientific treatises are 
intended merely to present scientific data. But any book 
designed to be used by high-school students as a text- 
book in science should have primarily the purpose of 
developing scientific ahility ; that is, ability to under- 
stand clearly scientific matters, to derive from known 
facts and laws other facts and laws, to pass logically from 
causes to effects or from effects back to causes, and, above 
all, to connect the practical matters of everyday life with 
the science involved. All mere scientific data should be 
entirely secondary to these objects. Those facts should 
be given which most clearly illustrate the laws and prin- 
ciples presented ; the laws and principles presented should 
be those which are most fundamental and farthest reach- 
ing, that appeal most strongly to reason, and have the 
greatest practical value. This is particularly true with 
physics, first because it is the basis, so far as the funda- 
mental, laws of nature are concerned, of all the other 
sciences ; and second because it is an intensely practical 
subject, bearing directly on the everyday life of all 
persons at all times. 

The authors have had in view such a text-book while 
producing this work. But the results obtained depend 
very largely upon the student, and some suggestions as 
to methods of study may be of value. 

4. Methods of studying Physics. — Many students come 
to the study of physics after a course in botany, geology, 
or some kindred subject, and find difficulty in adapting 
themselves to the different methods required in physics. 
The spirit of physics once realized, however, the diffi- 



4 INTRODUCTION 

culty ceases. Biological studies require a familiarity 
with many names of things and many relations among 
various things ; the scientific ability sought is, partly, 
such as will enable the student to identify various objects 
and group them into classes. While the reasoning powers 
are much called in play, the mind, perhaps unintention- 
ally, tends toward memorizing. 

In physics, however, the tendency should be entirely 
the other way. While many terms peculiar to physics 
must be learned and some facts memorized, in order to 
form a basis foi^ the study, yet the student should strive as 
rapidly as possible to make such work entirely secondary ; 
and should direct his attention, first, to a clear under- 
standing of the matter presented^ and, second, to appliea- 
tions of it to other subjects. For instance, when a fact is 
stated, the aim should be, not to memorize the mere fact, 
but to understand its full significance ; how does it bear 
on the facts and laws already studied, or on those being 
discussed, or on the affairs of life? Once its relation to 
such matters is clearly thought out, no effort will be 
required to keep it in mind, and far more will be accom- 
plished than the acquiring of a mere knowledge of the fact. 
When a law is stated, facts supporting it should be called 
up from past experiences, its application to everyday life 
should also be considered, and the student should aim to 
understand why the law must be true if the fundamental 
principles of physics are accepted. He should, if possible, 
see the connection between the law and the fundamental 
principles so clearly that belief in the law becomes irre- 
sistible. No effort will then be required to remember the 
law ; and, even if forgotten in time, the mental develop' 
ment will be effective always. 

In brief, the student should constantly keep in mind 
that the data of physics are much easier to remember if 



INTROBUCTION 5 

they are interpreted in terms of past experiences, every- 
day events, and the fundamental principles and laws ; 
and that such interpretations are far more valuable than 
the mere acquisition of data, not only in the study of 
physics itself, but also in securing success in any line 
of life. 



CHAPTER I 

MATTER 

SECTION 1. STRUCTURE OP MATTER 

5. Matter. — As we look about us we see all sorts 
of objects made of different materials, each taking up 
more or less space. Matter is a term which applies to 
each of them, without reference to its size, shape, or 
material. Thus, matter may be defined as anything 
which occupies space, as wood, iron, water, or air; and 
we study matter by studying the various objects around us. 

6. Size of Objects. — One of the first things which we 
notice in regard to an object is its size, or magnitude. 
Every portion of matter has three dimensions, — length, 
breadth, and thickness. These dimensions we frequently 
wish to measure ; and to measure any magnitude we must 
compare it with some unit. If one desires to measure the 
length of a plot of ground, he often paces it to see how 
many of his steps are equal to the length of the plot. In 
this case the length of one of his steps is the linear unit 
with which the larger dimension is compared. If he 
wishes to determine the capacity of a cask, he deter- 
mines how many times it will contain the contents of 
some unit, as a gallon or a quart measure. 

The yard and the meter are the common units for linear 
measure; the square foot, square yard, and square meter 
for surface measure; the cubic foot, cubic yard, and cubic 
centimeter for volume measure; and the quart, gallon, and 
liter for measuring the capacity of receptacles for holding 
liquids. 

6 



§§5-12 J STRUCTURE OF MATTER 7 

7. The Meter. — The meter is the distance between 
two marks uj)on a platinum-iridium bar kept at Paris, 
and its length was obtained by carefully determining the 
length of a meridian circle passing through Paris, and 
dividing it by 40,000,000. Various multiples and 
divisions of the meter are used in measuring larger or 
smaller distances (see table, p. 369). The centimeter, 
which is one one-hundredth of the meter, is the unit 
most used in scientific work for the measurement of 
small magnitudes. 

8. The Yard. — The English unit of linear measure is 
the yard, and is the distance between two marks upon 
a platinum bar kept at London. The derivation of this 
unit is perhaps doubtful ; at any rate it has not the sig- 
nificance of the meter. With the multiples and divisions 
of the yard we are familiar. 

9. The Liter. — The liter is the metric unit of liquid 
measure, and its capacity is the same as that of a cube one- 
tenth of a meter, or one decimeter, on a side. It is a 
little greater than the quart. 

10. Surfaces and Volumes. — Surfaces are measured in 
terms of the square of any of the linear units, and volumes 
in terms of the cube of the units. The centimeter is the 
linear unit which will most often be used in this work. 

11. Weight of Objects. — When we pick up any ordinary 
body we are conscious of its weight, or that it requires an 
effort to keep it from falling, and that such effort varies 
greatly with different bodies. The force that we must 
overcome in lifting such a body is the pull of the earth upon 
it, or gravity. Weight is the measure of this for ce^ and the 
units of weight are the gram, the kilogram, and the pound. 

12. The Gram. — If we are to have a definite unit of 
weight, we must use as a standard a definite volume of 
some substance under conditions which shall be invari- 



8 MATTER [§§ 12-17 

able. The volume chosen is the cubic centimeter, and 
the substance pure water at its temperature of greatest 
density. The gram is the name of this unit, and it is the 
weight of a cubic centimeter of water at a temperature 
of 4° Centigrade. 

13. The Kilogram. — The kilogram is another metric 
unit of weight, and is the weight of one cubic decimeter 
of pure water at 4° Centigrade, and thus equals one 
thousand grams. 

14. The Pound. — The pound is the English unit of 
weight, and is the weight of a piece of platinum kept at 
London as the standard. 

15. Structure of Matter. — All matter is supposed to be 
made up of exceedingly small particles, or units, called 
molecules. A piece of marble may be ground to powder 
so fine that a breath of air will stir it up and carry more 
or less of it away, yet each of these minute particles is 
made up of a great number of molecules. A piece of ani- 
line the size of a grain of sand when dissolved in water will 
color quarts of water quite perceptibly, showing that there 
are particles of the aniline in every drop of the water. 
This experiment shows the minuteness of the particles 
into which a solid may be divided; and in this case the 
individual molecules are probably separated. 

16. The Molecule. — A molecule may be defined as the 
smallest particle of matter which can exist by itself. 
Molecules are so small that millions of them are required 
to make an object large enough to be seen with a good 
microscope. 

17. Mass. — Any quantity of matter which is composed 
of molecules is called a mass. Matter exists in several 
states or conditions. If the mass has a definite shape, 
which is not easily changed, it is called a solid, as wood, 
coal, iron, etc. If the mass changes its shape readily and 



§§ 17-18] STRUCTURE OF MATTER 9 

conforms to the sliape of the containing vessel, it is called 
a liquid, as water. If it tends to expand indefinitely, and 
so fills all the space allotted to it, it is called a gas, as air. 

18. The Kinetic Theory. — The molecules composing any 
mass of matter are supposed to be in a state of constant 
vibratory motion, being held together, to a greater or less 
degree, by molecular attraction. The molecules attract 
each other very much as a magnet attracts a nail or other 
small piece of iron, but with this difference : the nail is 
drawn to the magnet and held in close contact; on the 
other hand, the shock of contact of the molecules causes 
them to rebound, or at least to change their direction or 
speed, and they then move away from each other until 
they strike other molecules, or until their attraction for 
each other overcomes this tendency to separate. The 
former will always happen within any mass, and the 
latter when the molecules are located upon the surface 
of a solid and bound outwardly. In the case of gases 
the molecules are supposed to move in straight lines 
until they collide with other molecules or the sides of 
the containing vessel. 

In liquids we have conditions between those of solids 
and gases, and these conditions vary greatly in different 
liquids and in the same liquid under different conditions. 
The molecules upon the surface of a liquid may vibrate 
so vigorously that many of them will overcome the attrac- 
tive force of the others and move off into space ; but in 
general we may say that the attractive force between the 
molecules of a liquid is greater than their kinetic tendency 
to separate, for the evaporation, or moving off, of the mole- 
cules at ordinary temperatures is comparatively slow. 

This theory of molecular motion in masses is called the 
Kinetic Theory of matter, and the supposed vibratory motion 
is called kinetic actioii of the molecules. 



10 MATTER [§§ 19-21 

19. Solids, Liquids, and Gases. — As lias been suggested, 
matter exists in three forms, — solids, liquids, and gases. 

A solid is a body which has a definite form or shape 
that is not easily changed, because the molecules com- 
posing the body do not readily change their relative 
positions. In solids the distance through which the mole- 
cules vibrate is very small, and the attraction of the 
molecules for each other is much greater than their ten- 
dency to separate by reason of their kinetic action. 

Liquids^ of which water is the commonest type, are sub- 
stances which have no definite shape, and conform readily 
to the shape of any vessel in which they may be placed. 
In liquids the kinetic tendency to separate and the molec- 
ular attraction nearly balance ; the latter, however, is 
somewhat stronger, as is shown by the fact that water 
forms into drops which hold together and have definite 
shapes. 

Gases are substances which change their shape as readily 
as liquids and also tend to expand indefinitely, so that a 
given quantity of a gas will expand and fill all the space 
that is allowed it. In gases the kinetic action of the 
molecules seems to have entirely overcome the molecular 
attraction, so that the molecules tend to move away from 
each other indefinitely. 

20. Atoms. — Every molecule is supposed to be made 
up of simpler units, or divisions, called atoms. A mole- 
cule of water is supposed to be made up of two hydrogen 
atoms and one oxygen atom ; a molecule of common salt 
is supposed to be made up of one chlorine and one sodium 
atom, and so forth. The atoms forming a molecule are at- 
tracted to each other and held together by atomic attraction, 
or chemism. 

21. Density. — We are familiar with the fact that a piece 
of lead or iron is heavier than a piece of wood of the same 



§§ 21-23J STUUCTURE OF MATTER 11 

size. This is clue to the difference in density of the vari- 
ous substances ; the iron contains more matter than the 
wood — it is denser. We have seen that the weight of a 
cubic centimeter of water is 1 g. ; and for convenience we 
take as our unit of mass the mass of a cubic centimeter of 
water, or a mass weighing 1 g. Hence we say the density 
of water is 1 g. per cubic centimeter. If a cubic centi- 
meter of iron weighs 7 g., we say its density is 7 g. per 
cubic centimeter, or, briefly, 7. In order to find the den- 
sity of a substance, then, we have only to divide its weight 
by its volume, though the weight should be in grams and 
the volume in cubic centimeters, and density may be defined 
as the mass of a cubic centimeter of the substance. 

22. Further Discussion of Mass. — As stated in Art. 17, 
any quantity of matter composed of molecules is called a 
mass of matter ; but by the mass of a body we mean the amount 
of matter that it contains, and this is determined by two 
things, volume and density. Other things being equal, 
the mass of a body is proportional to its volume ; and also, 
volume remaining constant, the mass is proportional to 
the density. Then the mass of a body is represented by the 
product of the numbers representiny its volume and deiisity. 

The units of mass are the same as the units of weight, 
viz. the gram, kilogram, and pound ; but, while the mass of 
a body is always the same anywhere in the universe, the 
pull of gravity for that body, and thus its weiyht^ may vary 
greatly, as we shall learn later. In ordinary laboratory 
work the terms mass and weight are practically sjmony- 
mous. With the same object they are always numeri- 
cally equal, and the mass is usually determined by weighing 
the object ; but there is a difference in nature which should 
be recognized. 

23. Physical and Chemical Changes in Matter. — Matter 
is subject to two kinds of changes, physical and chemical. 



12 MATTER [§2:3 

A physical change is a change in which the nature or 
structMve of the molecule is not changed. When ice is 
melted or water frozen, a physical change takes place ; 
for, while to outward appearance the matter is not the 
same, we have reason to believe that the molecules remain 
unchanged. 

A chemical change is a change in which the structure of 
the molecule is changed. That is, the number, arrange- 
ment, or kind of atoms composing the molecules has 
changed, and thus the nature of the whole mass has been 
changed. When wood burns, zinc dissolves in an acid, or 
iron rusts, a chemical change takes place. 



EXERCISES 

1. How many cubic centimeters in a rectangular block 
measuring 2 x 8 x 12 dm. ? 

2. How many cubic inches does it contain ? how many cubic 
yards ? (Refer to tables, p. 369.) 

3. How many cubic meters in a sphere 2 in. in diameter ? 

4. How many grams does a liter of water weigh ? a cubic 
foot of water ? 

5. How many pounds in 2400 g. ? in 34 g. ? 

6. How many pounds in a cubic yard of water ? 

7. If a liter of sulphuric acid weighs 1800 g., what is the 
density of the acid ? 

8. What is the density of a cubic foot of stone, weighing 
174 lb. ? of a cubic foot of wood weighing 38 lb. ? 

9. If mercury is 13.6 times as dense as water, what is the 
density of mercury ? 

10. If the density of alcohol is .8 g., and it is .9 times as 
heavy as an equal vohune of benzine, what is the density of 
benzine ? 

11. If the alcohol is 621 times as heavy as an equal volume 
of air, what is the density of the air ? 



§§24-27] PROPERTIES OF MATTER 13 

SECTION 2. PROPERTIES OF MATTER 

24. Properties of Matter. — Matter has certain charac- 
teristics, or properties, some common to all forms of matter 
and others which are peculiar to certain kinds. The more 
important ones are Extension, Indestructibility, Inertia, 
Porosity, Elasticity, Hardness, Tenacity, Malleability, 
Ductility, and Cohesion. 

25. Extension. — Extension is that property of matter 
by virtue of which it occupies space, or has dimensions, 
— length, breadth, and thickness. 

26. Indestructibility. — Careful experiment has shown 
that although the form or condition of matter may be 
more or less easily changed, yet no matter can be de- 
stroyed. When we burn a stick of wood, a large part of 
it apparently disappears, and the impression might be 
that some of the material is actually destroyed ; but the 
fact is that the elements of the wood have united with 
oxygen to form other substances — carbon dioxide, and 
water. Many more examples might be given, but suffice 
it to say that the quantity of matter in existence is always 
the same whatever the changes in condition; and this 
property is called iyidestruetibility^ or conservation, of 
matter. 

27. Inertia. — Inertia is that property of matter by 
virtue of which a body tends to persist in its condition of 
rest or uniform motion. 

Attach a light cord to a car or to a sled resting on the ice. 
A sudden jerk will break the cord before it can overcome 
tlie inertia of the body. Pull lightly and steadily, and the 
body is easily set in motion. Again, set the body in mo- 
tion, and attempt to stop it suddenly, and the cord will 
break before the inertia of motion is overcome. Another 
good illustration is to suspend a heavy iron ball or sack of 



14 



MA TTER 



[§§ 27-28 




sand to the ceiling by means of a cord but little stronger 
than is required to support the weight. Attach another 
piece of the same cord to the under side of the weight, and 
pass it through a hole directly beneath in a shelf or table, 
so that the weight cannot fall upon the 

^ ^ hand (Fig. 1). A quick jerk on the 

under cord will invariably break it be- 
fore the inertia of the weight can be 
overcome ; while a slow, steady pull 
will always break the upper cord. 

Every one experiences daily the re- 
sults of inertia : A running person can- 
not stop quickly, as his inertia forces 
him onward ; a door slams when pushed 
too hard; persons riding in cars are 
thrown forward or backward as the car 
stops or starts; as the car is stopping 
it is difficult to walk toward the rear 
end ; the small boy throws at a mark a stone rather than 
a roll of paper, but he kicks with his bare feet the paper 
rather than the stone. 

The inertia of any body is proportional to its mass, and 
hence to its weight ; so to determine the relative inertias 
of bodies we have only to determine their relative weights. 
28. Porosity. — What has already been said in regard 
to the structure of matter indicates that there are spaces 
between the molecules. These spaces are called pores, 
and this general property is called porosity. 

Fill a Florence flask with water to a certain mark on the 
neck. Pour out about one-third of the water, and pour in 
exactly the same volume of alcohol, and shake well. It 
will be found that the mixture does not fill tlie flask to the 
original mark. This fact strongly suggests, at least, that 
the molecules of alcohol have g^one to some extent to fill 



Fig. 1. 



§§28-31] PROPERTIES OF MATTER 15 

the spaces between the molecules of water, or the con- 
verse. A similar experiment is to fill the flask with water 
as before and then slowly sift into it finely powdered sugar 
or salt. It will be found that a considerable quantity 
may be sifted in before the level of the water is raised 
at all. 

29. Elasticity. — Elasticity is that property of matter by 
virtue of which bodies tend to resume their original form 
or volume, when their form or volume has been changed 
by the application of some force. Elasticity of shape is the 
tendency of a body to resume its former shape when this 
has been forcibly changed. A steel spring or a rubber ball 
returns almost exactly to its former shape after a forcible 
change. If, however, the change in form is too great, a 
body does not return to its original shape. The point 
where a body begins to change its shape permanently is 
called the elastic limit. Elasticity of size, or volume, is 
the tendency of a mass of matter to return to its original 
volume when original conditions have been restored after 
having its volume changed by a change of conditions. A 
quantity of air, if subjected to a high pressure, becomes 
much reduced in volume ; but as soon as the pressure is 
removed, and original conditions restored, it returns to its 
original volume. 

30. Hardness. — Hardness is that property of matter by 
virtue of which a body resists any attempt to force a pas- 
sage among its molecules, or in other words, any attempt 
to scratch it. We are familiar with the great difference in 
the hardness of substances. The diamond is the hardest 
known substance. Hardened steel, as represented by a 
file, is one of the hardest of substances. Butter is soft, 
and is softer when warm than when cold. 

31. Tenacity. — Tenacity is that property of matter by 
virtue of which a body resists any force that tends to pull 



10 MATTER [§§ 31-35 

it apart. Tenacity depends upon molecular attraction, 
and varies greatly in different substances, as is illustrated 
by strips of paper and by steel wire. 

32. Malleability. — Some substances, as iron and lead, 
may be rolled or hammered into very tliin slieets. This 
property is called malleability. Gold is the most malle- 
able of all substances. It may be hammered into such 
thin slieets that 300,000 of them piled upon each other are 
not more than one inch thick. 

33. Ductility. — Some substances, as copper and silver, 
may be drawn into very fine wire. This property is called 
ductility. Red hot glass is a good example of a ductile 
substance. Take a small glass rod, and after warming it 
gradually, hold it in the flame of a Bunsen burner, and 
keep it rolling until it is red hot ; then remove it from the 
flame, and pull the ends as far apart as possible. The 
result will be a fine glass thread or wire. Fine wire is 
made by drawing out larger wire. 

34. Cohesion and Adhesion. — Cohesion and adhesion are 
two forms of molecular attraction which seem to be exactly 
alike. If molecules of any substances, like or unlike, are 
brought close enough together, they will attract each other 
with varying degrees of intensity, according to the sub- 
stances and their distance from each other. This property 
of matter which causes the molecules to attract each other 
is common to all kinds and forms of matter. The attrac- 
tion of unlike molecules for each other is often greater 
than that between like molecules, but the two forms are 
the same in nature, and for convenience only we distin- 
guish between them. 

35. Cohesion. — Cohesion may be defined as the attrac- 
tion of like molecules for each other. If cohesive force 
were destroyed, blocks of iron, rocks, and in fact all solids, 
would crumble to powder by their own weight. A drop 



§§ 35-37] PROPERTIES OF MATTER 17 

of water upon a perfectly dry or oiled surface tends to take 
a spherical form, because the cohesion among the mole- 
cules of water draws them as closely as possible together. 
Elasticity is merely an effect of cohesion ; when the 
molecules are pulled apart, cohesion tends to draw them 
together. Similarly with hardness and tenacity, substances 
are hard and tenacious because cohesion resists the pulling 
apart of the molecules. Substances are malleable or duc- 
tile when the cohesion is such as to allow the molecules to 
be separated so as to change their positions with relation 
to each other without tearing them asunder. 

36. Adhesion. — Adhesion is the force of attractio^i of 
unlike molecules for each other. It is the force that 
causes the gummed stamp to stick, or the hand to remain 
wet when withdraAvn from the Avater, or sealing wax to 
stick on an envelope. 

Cohesion and adhesion act only through insensible or 
infinitesimal distances. Lay together two freshly cut sur- 
faces of lead, or paraffin, or plate glass, and they will not 
stick ; but press them together strongly with a twisting 
motion and they will cohere strongly. If two pieces of 
window glass are placed together they will not cohere 
appreciably, even when pressed ; but if the surfaces in 
contact are wet, they will adhere strongly. This is be- 
cause the water fills up the slight hollows in the surfaces 
of glass. 

37. Surface Tension. — A property of matter which is 
peculiar only to the surfaces of liquids, and which is also an 
effect of cohesion, is surface tension* If a cambric needle is 
very carefully laid upon the surface of a glass of water, it 
will float ; and if one looks through the glass, just below the 
surface of the water, he will see that the needle is floating 
in a depression on the surface, wdiich is greater in dejjth than 
the diameter of the needle., and apparently floating or lying 



18 MATTER [§§ 37-38 

upon an elastic membrane stretched over the surface of 
the water. If a drop of alcohol is dropped into the water 
on one side of the needle, the needle will be suddenly 
pulled away from tlie place where tlie''d^opi. strutik'.as if 
the elastic film had broken at that point. 

This surface tension, or surface film, is supposed to be 
caused by the different conditions in which the molecules 
upon and below the surface are placed. The molecules 
below the surface are attracted with equal force in all direc- 
tions, while those upon the surface are attracted only down- 
wa7'd and laterally ; the result is that the molecules upon the 
surface are bound together to form a film over the surface 
of the Avater. The molecular attraction in alcohol is much 
weaker than in water, and so when the drop of alcohol 
strikes the water it weakens the film, which, by its elasticity, 
pulls away from that point. If a small wooden boat is 
placed on the water, and alcohol is alloAved to run slowly 
from a groove in its stern into the water, the film behind 
the boat will be broken or weakened, and the boat will be 
drawn forward through the water. 

When a clay pipe is dipped into soapsuds, a portion of 
this surface film is picked up, and its great elastic limit 
is proven by the size to which a bubble may be blown. 
With care water may be poured into a tumbler until it 
rises a millimeter or two above the edge of the tumbler, 
as the surface film prevents an overflow. 

38. Capillarity. — A property of matter peculiar to liq- 
uids in contact with solids is that of capillarity. If a 
clean glass test-tube is partly filled with water, it will be 
seen that the surface of the water is not level, but rises 
around the edges of the tube, as shown in section in Fig. 
2. This curved surface is called a meniscus, and is caused 
by the adhesion between the waiter and the clean glass. 
Any such plienomenon is called capillarity. 



§§ 38-40] 



PROPERTIES OF MATTER 



19 



Thrust a clean strii^ of glass into a dish of water, and the 
water will rise around the glass, as in Fig. 3, and when the 

glass is withdrawn it will be wet. Now set a 

small glass tube in the water (Fig. 4), and the 
water will rise in the tube considerably above 
the level of the surrounding water. These same 
pieces of glass set in mercury will cause a depres- 
sion in the mercury, as shown in Figs. 5 and 6, 
and when withdrawn from the mercury they will 
not be wet. Clean zinc or lead in mercury will 
cause a rise like that of water around glass, and when they 
are withdrawn they will be wet with the mercury. 

Oiled glass causes a depression in Avater, and is not wet 
when withdrawn. In the case of tubes, the smaller the 



Fig. 2. 




J?'1G. 4. 



Fig. 5. 



Fig. 6. 



tube the higher the rise or the greater the depression. 
We find also that cold water rises higher than hot, for, 
as we shall find later, heat tends to destroy molecular 
attraction. 

39. Laws of Capillarity. — Liquids ivet a solid when the 
adhesion hetiveen the liquid and the solid is stronger than the 
cohesion in the liquid. 

Liquids rise around solids that they ivet^ ayid are depressed 
hy those that they do not ivet. 

In ca'pillary tuhes^ the smaller the tube the greater the rise 
or depression. 

Heat tends to destroy capillarity. 

40. Effects of Capillarity. — We have many natural 
phenomena caused by capillary action, and many applica- 



20 MATTER [§40 

tions of the action to the arts and sciences. The soil 
near the surface is kept moist in dry weather by capillary 
action causing moisture from below to rise, and the farmer 
keeps the soil stirred so the moisture will not rise too 
readily, as otherwise the roots of the plants would dry up. 
A sponge or cloth soaks up water, just as a blotter soaks 
up ink, because of the capillary action ; and oil rises in 
the lamp-wick for the same reason. Many scientific 
experiments are assisted — and many interfered wdth — 
by this action. 

EXERCISES 

1. Which has greater extension, a liter of water or a block of 
wood 9 X 72 X 16 centimeters ? 

2. When a lead-pencil is burned, it is destroyed. Is the wood 
destroyed ? Is the matter composing the wood destroyed ? 

3. Which has more inertia, a liter of alcohol, with density 
of .81, or a stone weighing 1.2 kg. ? 

4. Why does a ball thrown horizontally continue to move 
horizontally after it leaves the hand ? 

5. Which has a greater elastic limit, steel or lead ? steel or 
rubber ? 

6. Of solids, liquids, and gases, which have elasticity of 
volume, and which of shape ? 

7. If water in a lead vessel is sufficiently compressed, it will 
ooze through the lead. What property of the lead is thus 
shown ? 

8. When a piece of glass removed from water remains wet, 
which force involved is stronger, cohesion or adhesion ? 

9. Why does capillarity cause water to rise higher in small 
tubes than in large ones ? 



CHAPTER II 
MOTION AND FORCE 
SECTION 1. MOTION 

41. Motion is change of position. When a train of cars 
is running from one station to another, it is continually 
changing its position on the track, and is said to be in 
motion. 

42. Direction of Motion. — It is evident that the change 
of position which we call motion may take place in any 
direction ; the train may go east, west, north, or south ; a 
ball may be thrown upward, downward, or in any other 
direction. And the direction of the motion may change ; 
the ball thrown horizontally gradually curves downward ; 
or if it strikes a hard surface, it bounds off in a very dif- 
ferent direction. 

43. Path of Motion. — The path of motion of any body 
is the route over which it travels. The railway track is 
the path of the train ; if a stone is dropped, its path is 
straight downward. 

The path of motion in any 
case may be represented by a 
line the direction of which 
indicates the direction of mo- 
tion, while its length indi- " fig^t 
cates the relative distance the 

body moves. Thus, if a boy walks south 10 ft. and then 
east 20 ft., his path may be represented by the lines AB 

21 



22 



MOTION AND FORCE 



[§§ 41-i4 




and BC in Fig. 7. It is immaterial how long the lines 
are, provided BO is twice as long as AB^ 20 being twice 
10. The arrows indicate the directions. 

44. Composition of Motions. — It frequently happens that 
we wish to determine what single straight motion will 
produce the same result as two or more separate motions. 

Thus, representing again the 
boy's path by AB and ^6^ in 
Fig. 8, he moves from A to 
C, and it is evident the re- 
sult would be the same if he 
walked straight from A to C 
along AC. And no matter 
how circuitous his path may have been in going from A 
to C, so far as mere change of position from ^ to C is 
concerned, the same result would have been produced if 
he had taken the path AC. Thus ^C^ is the resultant 
path of the other paths, and is equivalent to them. And 
in any case the composition of motions is the combining 
of two or more motions into one resultant motion that is 
their equivalent. 

The resultant of two or more simultaneous motions may 
be found in the same way. Thus, suppose the boy walks 
10 feet south on the deck of 
a steamer, and as he walks 
the steamer goes 20 feet east; 
if A (Fig. 9) is the starting- 
point with reference to the 
surface of the earth, C will be 
the point reached at the end 

of the time. In this case A will be not only the result- 
ant but also the actual path travelled with reference to 
the surface of the earth. Because, when he lias walked 
to d^ for instance, the boat has carried him east twice the 




Fig. 9. 



§§ 44-46] MOTION 23 

distance Ad^ or to g; so he will actually be in the path AC. 
And similarly with any other distance south that he walks. 
The magnitude of the resultant may be found by geom- 
etry, if the angle formed by AB and ^6* is a right angle. 
Thus, in this case, AC= V lU^ + 20^. If the angle formed 
by the motions is oblique, the resultant may be found by 
trigonometry, or, approximately, by measuring the lines 
and finding the length of the resultant with reference to 
the others. 

45. Resolution of Motions. — Conversely, we sometimes 
wish to find the component motions when the resultant is 
given; that is, to resolve one straight motion into two or 
more other motions that will be its exact equivalent. This 
is called the resolution of motions. In the above case, as 
the same result is reached when the boy walks along ABO 
as along A C, we may resolve the motion A C into the com- 
ponents AB and BO^ or into as many other motions as we 
please, provided, only, that the first motion begins at A 
and the last ends at 0. 

As we can thus resolve any motion into any number of 
components, in order to determine any of the components, 
the directions and magnitudes of the others must be 
known. For instance, we may be required to resolve AQ 
into two components; if it is known that one of them is 
AB^ the other must then be BC. 

46. Speed is the rate at which a body is travelling at 
any specified time; the distance it would travel in a given 
time if it continued travelling uniformly. A person may 
say a passing street car is going at the rate of ten miles 
an hour. He does not mean it will travel ten miles in an 
hour; it may change its speed at any instant. He means 
its speed is such that it would travel ten miles if it con- 
tinued at the same rate for an hour. This is frequently 
called instantaneous speed. 



24 MOTION AND FORCE [§§47-49 

47. Constant Speed. — If the body continues to travel at 
the same rate, going neither faster nor slower, we say its 
speed is uniform, or constant. This does not mean that the 
body is travelling with any particular speed, but simply 
that its speed is not changing. 

In case of constant speed the actual speed is equal to the 
total distance travelled divided by the time taken. 

48. Average Speed. — A body may move from one 
position to another in a certain time, but its speed 
during the time may not be constant ; it may increase 
or decrease. In such case we may speak of the average 
speed, which is equal to the total distance travelled 
divided by the time, the same as its speed would be if 
it were constant. 

49. Velocity. — Whenever we have motion, then, two 
factors are involved, the speed of the motion and its direc- 
tion. Velocity is the rate at which the motion is taking 
place. When the velocity is known, the entire motion is 
known, — the speed and the direction. To illustrate the 
difference between speed and velocity, consider a horse 
trotting around a circular track ; we may say its speed 
is a mile in three minutes; but we cannot say that 
of its velocity, as the direction of its motion is con- 
stantly changing, and this as well as the speed affects the 
velocity. But if the track is straight, running from 
north to south, w^e may say the speed of the horse is a mile 
in three minutes and its velocity is a mile in three minutes 
toward the south. 

In case of constant velocity neither the speed nor the 
direction of motion is changing; it is constant speed in 
one direction. 

Average velocity is the total change in motion divided 
by the time taken. If there is no change in direction, it is 
the average speed in one direction. 



§§ 50-51] MOTION 25 

50. Momentum. — If two bodies, one having a mass of 
one gram and the other of ten grams, have equal velocities, 
it is evident that each gram of the larger has just as much 
motion as the one-gram mass, and the total amount of motion 
of the larger mass is ten times that of the smaller. At the 
same time, if the velocity of a gram mass is ten times that 
of another, it is evident that the total amount of motion of 
the one is ten times that of the other. So, if we consider 
the total amount of motion, or the quantity of motion, in 
any body, we must consider the mass and the velocity of 
the body ; and as the quantity is proportional to each, the 
product of the mass and velocity gives the total quantity 
of motion, or, as it is called, the momentuyn^ of the body. 
The momentum of any body, then, equals its mass times 
its velocity. 

51. Acceleration. — When the train pulls out of the 
station, it goes faster and faster for some time ; and as it 
approaches the next station, it goes slower and slower. Its 
velocity increases in the one case and decreases in the 
other; its motion is accelerated and then retarded; and 
the rate at wdiich its motion is accelerated or retarded is 
called its acceleration. Thus, if the train goes at one 
instant ten feet per second, and a second later fifteen feet 
per second, its acceleration is five feet, because the rate 
at which its velocity increases is five feet per second. 
If it takes two seconds to increase its velocity six feet, 
its acceleration is three feet. Acceleration^ then, is the 
time-rate of change of velocity. 

The acceleration is j^ositive if the velocity increases, and 
negative if it decreases. It is uniform, or constant, if the 
velocity gained or lost is the same each second. Thus, if the 
velocity continues each second to gain five feet per second, 
its acceleration is constant. In such case its average veloc- 
ity is one-half the sum of its initial and its final velocity. 



26 MOTION AND FORCE [§§ 52-53 

EXERCISES 

1. Indicate by diagram the resultant path of a man walking 
east 20 ft. on a steamer which carries him at the same time 
south 30 ft., and determine the distance he travels. 

2. Also when he walks 8 ft. east and the steamer moves 16 ft. 
north. 

3. If a person walks southeast 32 ft., how far east will he 
move ? how far north ? how far south ? 

4. A bullet shot vertically upward rises 2000 ft., and while 
in the air it has an average speed of 22. How long before it 
strikes the ground ? 

5. A ball rolling down an inclined plane has no velocity at 
the beginning, and a velocity of 5 ft. at the end of the first 
second. AVhat is its acceleration ? What would be its velocity 
at the end of 4 sec. if its acceleration was constant ? 

6. If its velocity were 80 at the end, what would be its average 
velocity ? 

7. An automobile travels due south 18 mi. in .7 h. What is 
its average speed per sec. ? its velocity ? 

8. When going at such velocity, it is brought to a standstill 
in 22 ft. ; what is its acceleration if it stops in 3 sec. ? 

SECTION 2. FORCE 

52. Cause of Motion. — So far we have given no atten- 
tion to that which causes bodies to move. What is that 
which causes bodies to begin moving, to continue moving, 
and to stop moving ? 

We have seen already that the i)roperty of inertia tends 
to keep bodies at rest and also tends to keep them moving 
uniformly when once they are started. Evidently, then, it is 
inertia that causes bodies to continue moving. So we have 
to consider only what produces or destroys their motion. 

53. Force. — We say when a ball is throAvn, that the 
force of the hand causes its motion ; when struck by a 



§§ 53-55] FORCE 27 

bat, that the force of the bat causes it to stop or change 
its motion, and when caught, that the force of the hands 
stops or destroys its motion. In fact, in every case, that 
which produces, changes, or destroys motion is called force. 
We find, however, that some forces do not affect motion 
at all. A person may push against a heavy table without 
moving it, and may push with no more effort against a 
light one and move it easily across the floor. If force is 
used in the latter case, it must be in the former. In the 
former case the force exerted tends to move the table, but 
is unable to do so. And in many other cases the forces 
exerted merely tend to produce or change motion. So we 
may say force is that which tends to produce, change, or 
destroy motion. And as producing or destroying motion 
is changing motion, we may say, briefly, force is that ivhich 
tends to change motion. 

54. Force of Gravity. — Whenever any object is pushed 
from the table, it falls to the floor. The motion of the 
object is changed, and evidently some force causes it to 
fall. It is so with all bodies left unsupported ; some force 
causes them to fall toward the earth. And this force is 
spoken of as the pull of the earth, or the force of gravity., 
or, briefly, gravity. But we find that not only all unsup- 
ported bodies fall toward the earth, but all supported 
bodies tend to move toward the earth; and we conclude 
that this is also the effect of gravity. Hence gravity is 
that force which constantly tends to move bodies toward 
the earth. 

55. Force of Gravitation. — It has been shown that 
the earth attracts not only terrestrial bodies, tending to 
move them nearer, but also the moon, the other planets, 
and the sun ; while they in turn attract the earth and each 
other, each tending to move the other toward itself. Still 
further, all terrestrial bodies attract each other. In fact. 



28 MOTION AND FORCE [§§55-59 

it is probably true that each body in the universe attracts 
every other body. And this attraction is called the force 
of gravitatio7i^ or, briefly, gravitation. 

Gravity, then, is a special case of gravitation, — that case 
in which the earth and terrestrial bodies are involved. 

56. Constant Force. — As its name implies, a constant 
force is one that acts constantly, and, unless otherwise 
specified, it is uniform. Gravity, for instance, is always 
acting on all bodies on the surface of the earth, and with 
practically uniform intensity; so it is a good example of 
a constant force. 

57. Impulsive Force. —This, as its name implies, is an 
impulse or a push or a blow. It acts for a short time only, 
like the force of a bat when it strikes a ball. It is not 
strictly a force, but is the effect of force. 

SECTION 3. LAWS OF MOTION AND FORCE 

58. If a ball is thrown horizontally when a strong wind 
is blowing, its path will curve not only downward because 
of gravity, but also side wise because of the wind. If the 
wind is not blowing, the ball will not curve side wise, and 
we must conclude that if gravity also were not acting, it 
would not curve downward, but would go straight ahead 
in the direction in which it first started. 

Having in mind these and many similar facts. Sir Isaac 
Newton proposed what are known as Newton's Laws of 
Motion; and as these laws have been shown to be univer- 
sally true, and are of much importance in science, they 
should be carefully considered. They are spoken of as 
the First, Second, and Tliird Law of jNIotion. 

59. First Law of Motion. — Every body continues in its 
state of rest or of unifor^n motion in a straight line unless 
compelled by an external force to change that state. 

For instance, the inertia of the ball causes it to remain 



§§59-61] LAWS OF MOTION AND FORCE 29 

at rest when lying on the ground ; but when it is thrown 
by the force of the hand, its inertia tends to cause it to 
move uniformly forward in a straight line, but the external 
force, gravity, compels it to curve downward. The law is 
frequently called the Law of Inertia, and may be called to 
mind by associating it with the word inertia. 

60. Gravity in such case is the external force which 
compels the ball to change its state of motion. Let us 
consider now how the motion of any body is affected by 
external forces. 

If the moving ball is struck by a bat, its velocity is 
changed both in speed and direction. The change in 
speed is apparently somewhat proportional to the force of 
the bat; and the direction the ball takes, when struck 
squarely, is that in which the bat is moving. These facts 
are strictly true in all cases, and they are covered by New- 
ton's second law. 

61. Second Law of Motion. — The change in motion is 
proportional to the applied force^ and takes place in the 
direction in ivhich the force acts. 

This law seems to be inconsistent with many facts. 
For instance, when a ball is thrown horizontally it curves 
gradually downward instead of going straight down in 
the direction in which the force of gravity acts, as it 
does when dropped. But this is because the ball has 
been thrown horizontally, and while going downward its 
inertia carries it horizontally. It certainly goes down- 
ward from the hand to the earth. In fact, it may be 
shown by experiment that it travels downward the same 
distance in just the same time that it does when dropped, 
although it travels horizontally a long distance in one case 
and not at all in the other. 

To show this, arrange an apparatus by which one ball 
may be driven forward horizontally the instant another 



30 MOTION AND FORCE [§§61-62 

ball is allowed to drop from the same height. It will be 
found that the balls will reach the ground at the same 
time. They will thus travel the same distance downward 
and in the same time. Here we have the impulsive force 
of the blow driving one ball horizontally, and the constant 
force of gravity pulling it downward. But the experi- 
ment shows that it travels to the ground in the same 
time it would if merely dropped. That is, the direction 
of the changed motion due to gravity is downward in the 
direction of the applied force, and the speed of the changed 
motion is exactly proportional to the force. 

So in every case, no matter how many forces may be 
acting on a body, if it is free to move, each force will 
produce just the same change in motion as if it were the 
only force acting ; it will cause the body to move in 
its direction and proportionally to its magnitude. Thus, 
with the ball thrown horizontally, if the wind is blowing, 
the ball will be forced sidewise as well as horizontally 
and downward ; and the distance it goes sidewise will be 
proportional to the force of the wind. Hence the law 
may be stated as follows : 

Every force acting on a body produces its own effect inde- 
pendently of every other force. 

62. There are several important consequences of this 
law, which we will now consider. 

Composition of Forces. — We have seen that two or more 
motions may be combined into one resultant that is their 
equivalent. Similarly, two or more forces may be combined 
into one resultant force that would produce exactly the 
same effect as tlie several forces, and the process is called 
the comjyosition of forces. 

In the first place, it is evident that a force may be repre- 
sented by a straight line, just as a motion may be ; the 
direction in which the line is drawn representing the 




§§62-63] LAWS OF MOTION AND FORCE 31 

direction in which tlie force acts, and the length of 
the line representing the magnitude of the force with 
respect to other forces represented in the same way. 
Hence, consider a foot-ball kicked simultaneously by 
two boys; suppose the force of one kick is sufficient 
to drive the ball from ^ to ^ 
(Fig. 10) and the other from 
A to C. While it is true that 
the forces act at the same time, 
yet we may, just as with mo- 
tions, consider the effects suc- 
cessively. Thus one kick, if alone, would drive the ball 
from A to B^ and then the other from B to D; the 
resultant path, according to the composition of motions, 
would be AD; and evidently the resultant force would 
be sufficient to drive the ball directly from A to J). 
So AI) represents the resultant force in direction and 
magnitude. 

Similarly, the resultant of any number of simultaneous 
or successive forces may be found by considering their 
effects successively, the resultant being always the line 
joining the beginning and the end of the total effect. 

63. Magnitude of Resultant. — The magnitude of the 
resultant force may be found just as the resultant motion 
is found. There are several cases, which we will consider 
briefly. 

If two forces act in the same direction, their resultant 
will be simply their sum. If they act in opposite direc- 
tions, their resultant will be their difference, acting in the 
direction of the greater force. If they act at right angles, 
the resultant may be found by geometry ; and if at any 
other angle, by trigonometry, or approximately, by meas- 
urement of the lines representing the respective forces. If 
more than tvfo forces are acting, it is necessary only to find 



82 



MOTION AND FORCE 



[§§ 63-6G 




the resultant of any two, and then the resultant of that 
resultant with a third, and so on. 

64. Resolution of Forces. — It is evident also that a 
single force may be resolved into two or more forces tliat 

are its equivalent, the two 
or more forces being called 
its components. \iAD(¥'\g. 
10) is the single force, AB 
and BD may be its compo- 
nents. Or, we may resolve 
it into as many forces as we 
please, with any directions or 
magnitudes, provided only 
that they may be correctly 

represented by lines so drawn as to form a continuous 

line from A to D, as ABOED (Fig. 11). 

65. Equilibrant. — When any number of forces acting 
on a body are prevented from moving the body by some 
other force, — some force which holds the acting forces in 
equilibrium, — this force is called the equilibrant with 
relation to the others. Hence the equilibrant of a single 
force would be one equal to it in magnitude but acting in 
the opposite direction, while the equilibrant of any num- 
ber of forces would be one equal and 
op})osite to the resultant of all the 
forces. 

66. Centrifugal Force. — When a 
stone tied to a string is whirled 
around the hand, there is a constant 
pull on the string, due to a tendency 
of the stone to move outward. This 
tendency is called centrifugal force, 

or tangentiarforce. It is merely an effect of the stone's 
inertia, and is not a force. Suppose at any instant the 




Fig. 12. 



§§ 06-68] LAWS OF MOTION AND FORCE 33 

stone is at A (Fig. 12), revolving aromicl ; it is for the 
instant travelling in the direction J.5, andits inertia tends 
to carry it along in that direction. But the string is pulling 
it in the direction A0\ hence the stone can travel along 
neither AB nor A 0, but must take the resultant path A C. 
And the pull in the string, which is called centrifugal 
force, is due to the tendency of the stone to fly off on the 
tangent to the circle. 

67. Effects of Centrifugal Force. — There are numerous 
effects of this so-called force noticeable in everyday life. 
It causes mud to fly from rapidly revolving carriage or 
bicycle wheels ; it causes sleds in going quickly around a 
corner to slide off sidewise ; it makes it necessary for the 
bicycle rider in going around curves to lean inward, so 
that his weight will hold the centrifugal force in equi- 
librium. Rapidly rotating emery wheels, and fly-wheels, 
even, have burst because of this force. The various 
planets of the solar system are kept from falling into the 
sun by this same force. It is applied in various ways 
in the arts to separate substances of different densities. 
Milk and butter are separated by being rapidly rotated in 
a suitable machine called a centrifugal separator ; clothes 
are dried in modern laundries by the same process, the 
moisture being driven by centrifugal force away from 
the clothes as they are rapidly revolved. 

68. Centripetal Force. — When the stone is whirled 
around the hand, it pulls on one end of the string, while 
the hand pulls on the other. The pull of the hand is 
called the centripetal force. It merely holds the centrifu- 
gal force in equilibrium, as the two forces are equal. It 
should be remembered, however, that while the centripetal 
force is actually a force, what is called centrifugal force 
is merely an effect of inertia, and strictly is not a force 
at all. 



34 MOTION AND FORCE [§§ 69-70 

69. Weight. — We are now in a position to understand 
clearl}^ what is meant by weight. Tlie Aveiglit of a body 
is its tendency to move toward the earth. Tlie force of 
gravity causes bodies to tend toward the earth ; but a 
body on the earth, say at tlie equator, revolves around the 
center of the earth as the earth rotates, just as the stone 
at the end of the string may revolve around the hand, and 
hence there is a centrifugal tendency to carry the body 
away from the earth. So at the equator the force of gravity 
and the centrifugal force are acting in opposite directions 
on the body, and the resultant of these forces determines 
its tendency to move, or its weight. The magnitude of 
the resultant is the difference between the two forces, and 
its direction is that of gravity, as gravity is much the 
greater of the two. This resultant, therefore, is the weight 
of the body. 

If the body were at one of the poles of the earth, there 
would be no centrifugal force, and its weight would be 
determined solely by gravity. At any place between the 
poles and the equator centrifugal force would be effective, 
though not exactly opposite to gravity, and it Avould 
increase as the body approached the equator. 

70. We now come to Newton's Third Law of Motion, 
which will also require some discussion. 

Third Law of Motion. — With every action there is alivays 
an equal and opposite reaction. 

When a boy shoots one marble against another, two effects 
are always noticeable : the marble that is struck is driven 
from its place, and the one that strikes has its motion 
changed. The former effect is the actioyi of the shooter 
on the stationary marble ; the latter effect is the reaction 
of the stationary marble on the shooter. The action is due 
to the inertia of the shooter tending to carry it straight 
ahead, and thus driving the other marble out of its Avay ; 



§70] LAWS OF MOTION AND FORCE 35 

the reaction is due to the inertia of the stationary marble 
tending to keep it stationary, and thus resisting the action 
of the shooter. 

And it is true in every case where we have an action of 
one body on another, that the body acted on always reacts 
on the body which acts on it. When a bat strikes a ball, 
the ball reacts on the bat ; the anvil reacts on the black- 
smith's hammer ; the foot-ball on the boy's foot. 

Let us consider now whether the action and reaction are 
equal, as the law states. If a billiard ball strikes squarely 
another at rest, the two balls exchange velocities, the striker 
coming to rest, and the other moving forward with the 
original velocity of the striker. Evidently the effect of 
one on the other is equal to the effect of the other on it. 
This may be shown by suspending two similar balls side 
by side, and pulling one sidewise and letting it swing down 
against the other; the one it strikes will be driven on, 
while the ball itself will stop ; the tw^o balls will exchange 
their states with reference to motion. When two persons 
pull against each other on a rope, it is evident that they 
exert equal forces, the stress on the rope necessarily being 
the same at all points ; the force of one is the action, while 
that of the other is the reaction. 

It is evident also in each of these cases that action and 
reaction are opposite in direction, as the law states. 

EXERCISES 

1. What is tlie resultant magnitude of two forces, one 8 kg. 
and the other 6 kg., acting in the same direction on the same 
point ? when acting in opposite directions ? when acting at 
right angles to each other ? 

2. In the last case, with which force does the resultant 
make the smaller angle ? If the two forces were equal and at 
right angles, what angle would the resultant make with each ? 



3G MOTION AND FOECE [§71 

3. If it requires a force of 32 lb. to push a lawn-mower 
when the handle forms an angle of 45° with the ground, how 
much force is required when the handle is horizontal ? In 
which case will the wheels be more likely to slip ? 

4. What is tlie downward pressure due to the hands when 
the handle is at 45° ? 

5. If the earth were to rotate around its axis in 12 lir. 
instead of 24, how, if at all, would the weight of a quart of 
water be affected ? how would its mass be affected ? 

6. Would an ordinary beam balance indicate any difference 
in weight ? would a spring balance ? 

7. Which of these balances indicate differences in mass ? 
which differences in weight ? 

8. Why is it well for engineers to slow up in going around 
curves ? AVhat is the purpose of raising the outer rail of the 
track at curves? 

9. Consider a stone attached to a string whirled in a circle 
around the hand ; how would increasing the mass of the stone 
affect its centrifugal force ? why ? 

SECTION 4. UNITS 

71. Fundamental Units. — In order to compare one length 
with another, we have seen that it is most convenient to 
compare each length Avith some unit length, and thus find 
the value of each in terms of the unit. It is just the same 
with velocity, force, and all other comparable quantities 
used in physics ; we need for each some unit in terms of 
which we can determine the quantity. If we are selling 
butter, we need some unit weight with which to compare 
the total amount of butter. And for convenience of com- 
parison the same units should be used by every one. But 
still further, for various reasons, the different units used 
should be as closely related as possible. For instance, 
taking length, surface, and volume, it is far better to have 
the unit of surface simply the square of the unit of length. 



§§ 71-75] UNITS 37 

and that of volume its cube, than to have the unit of length 
one centimeter, that of surface, say, one square foot, and of 
volume one cubic inch. 

To these ends a system of units has been adopted in all 
sciences, and somewhat generally throughout this and many 
other countries. This system is based on what are called 
fundamental units. These are the units of length, mass, 
and time. All other units are based on these, as it happens 
that all quantities involved in science can be expressed 
either directly or indirectly in terms of length, mass, and 
time. 

72. Metric System. — The most general use of this rela- 
tion of units is embodied in wdiat is known as the metric 
system, which has for the unit of length the meter, and 
of mass the gram, both of which we have considered, 
and for the unit of time the second, with which we are all 
familiar. 

73. C. G. S. System. — But in physics, the meter being 
inconveniently long for many purposes, a special form of 
the system, based on the centimeter, the gram, and the 
second, and known as the C. G. S. system, is mainly used. 
It is this S3^stem wdiich will be used, unless otherwise 
specified, throughout this book. 

74. Derived Units. — All units other than the funda- 
mental units are called derived units, as they are derived 
from these fundamental units. The method of derivation, 
however, in many cases is beyond the scope of this work ; 
and in taking up new units they will be based on the 
fundamental units or on any units previously discussed. 

75. Unit of Speed. — As speed is the distance a body 
moves in a given time, and as distance is measured in units 
of length, the most convenient unit of speed is a distance 
of unit lengtli travelled in unit time ; and in the C. G. S. 
system a distance of one centimeter in one second. That 



38 MOTION AND FORCE [§§75-76 

is, a body travelling at the rate of one centimeter per 
second is travelling with unit speed. 

The Unit of Velocltij would necessarily be a unit of 
speed in a definite direction. 

76. Use of Units. — Perhaps a short discussion of the 
use of units in problems will aid in an understanding of 
the more difficult units that are to follow, and also in 
solving problems. In case of velocity, if the body is trav- 
elling at the rate of 100 units of length in 20 sec, its 
velocity is 100 divided by 20, or 5 units, because that is 
the number of units of length it would travel in one second. 
We do not, however, divide 100 cm. or ft. by 20 sec, but 
divide simply the quantity which represents the number 
of units of length by the quantity which represents the 
number of units of time, and we get another quantity, 
•which represents the number of units of velocity. The 
value of the units of velocity depends on the value of the 
other units ; thus, in the above case, if it is known that 
the C. G. S. system is intended, the velocity is 5 cm. per 
second ; if the distance is in feet, the velocity would be 
5 ft. per second; and, as there are 30.48 cm. in a foot, the 
latter velocity would be that many times the former, 
although in each case the velocity is 5 units. 

To assist in working problems, equations showing the 
relations among the various quantities involved are fre- 
quently used. Thus : 

Velocity = ; or using the initial letters, v= —, 

time t 

But it is considered better for the students themselves to 

derive such equations when the derivation is sufficiently 

simple, and for this reason no equations will be given 

except those the derivation of which is beyond the scope 

of this work. 

Frequently one quantity varies directly or inversely as 



§§ 76-79] UNITS 39 

another. Thus, velocity varies directly as distance and 
inversely as time. That is, if the distance is increased, 
time remaining the same, the velocity is increased corre- 
spondingly ; as the distance becomes greater, the velocity 
becomes greater. But if the time is increased, distance re- 
maining the same, the velocity is decreased correspondingly; 
as the time becomes greater, the velocity becomes less. 

77. Unit of Momentum. — As the momentum of any body 
is its quantity of motion, momentum is proportional to the 
mass and also to the velocity, and the simplest unit of 
momentum is a unit mass having unit velocity. In the 
C. G. S. system the unit becomes equal to a gram of matter 
having a velocity of one centimeter per second. 

78. Unit of Acceleration. — As acceleration is the in- 
crease of velocity in a given time, the acceleration of any 
body is proportional to its increase in velocity ; it varies 
directly as the increase in velocity. But just as it takes 
time to travel any distance, so it takes time to increase 
velocity. A bicycle rider cannot increase his velocity 
instantly ; and the greater the increase in velocity, the 
greater the time required. So time is an important factor 
in acceleration, and the shorter the time taken to increase 
the velocity, the greater the acceleration. Acceleration, 
then, varies inversely as the time, and it equals the in- 
crease in velocity divided by the time. 

Hence the unit of acceleration used is unit increase of 
velocity in unit time. 

79. Absolute Unit of Force. — We have seen that force 
is that Avhich tends to change the motion of matter. Now 
it is evident that it will require ten times as much force 
to change the motion of ten grams as it will to change 
the motion of one gram, provided the changes are equal in 
amount. So the amount of force involved is proportional 
to the mass which has its motion changed. At the same 



40 MOTION AND FORCE [§§ 79-«l 

time it is evident the greater the change in motion — that 
is, the greater the acceleration — of any body, the greater 
is the force involved. The greater the increase in velocity 
of a bicycle in a minute, the greater the force required 
of the rider. Hence the force required to accelerate any 
mass varies directly as the mass and as the acceleration 
produced ; the total force being equal to the magnitude 
of the mass times the magnitude of the acceleration pro- 
duced. And the unit of force usually used in science is 
a force sufficient to produce unit of acceleration in unit 
mass (or to impart unit of momentum to a body in one 
second). 

This unit is called the absolute unit of force to distin- 
guish it from the gravity units discussed below, and 
because it is absolute^ — unconditional. The value of the 
unit of course depends on the value of the units of mass and 
acceleration used : so we may have many units of this class. 

80. Poundal. — As the absolute unit of force is of much 
importance in science, and as it is somewhat difficult to 
clearly conceive, it will be w^ell to discuss briefly both the 
English and the metric unit. The English unit is called the 
Poundal^ and it is that force which will produce in a mass 
of one pound a unit of acceleration based on the foot. 
That is, if the mass of one pound at rest be perfectly free 
to move, — if there be no resistance to its motion but its 
inertia, — a force that, acting on it for one second, will give 
it a velocity of one foot per second, is equal to one poundal. 
Or if the pound mass is in motion, a force that is sufficient, 
if it should act for one second, to change the velocity of 
the mass one foot per second, is equal to one poundal. It 
is immaterial whether the velocity is increased or decreased, 
as in either case the inertia is overcome. 

81. Dyne. — In the C. G. S. system the absolute unit 
of force is called the Dyne. It is that force which will 



§§ 81-82] UJ^ITS 41 

produce in a mass of one gram a unit of acceleration 
based on the centimeter. Or, similar to the poundal, 
it is that force which, acting for one second on a mass 
of one gram, will change its velocity one centimeter per 
second, if the mass be perfectly free to move. 

To illustrate : if a mass supported by the hand is released, 
it is then perfectly free to move ; that is, nothing resists its 
motion but its own inertia. It at once begins to move 
toward the earth because of the force of gravity ; this 
force produces in the mass, then, a certain velocity ; it 
increases its velocity from nothing to a certain amount — 
it accelerates it. Now, if at the end of one second the 
force has given it a velocity of one centimeter per second, 
it has given it an acceleration of one unit ; and if the mass 
is one gram, the force is one dj^ne. 

But, as we shall see later (Art. 109), the force of grav- 
ity acting in this manner would produce an acceleration 
of about 980 centimeters per second ; hence the force would 
equal 980 dynes. 

82. Gravity Unit of Force. — We find, then, that the 
force of gravity acting on a gram mass is equal to 980 
dynes. This, of course, is true whether or not the mass 
is free to fall. But as tlie gram mass is our unit of 
mass, and as the force existing between it and the earth 
is very frequently referred to, it becomes inconvenient to 
express the magnitude of the force by such a large num- 
ber, and a simpler unit is desirable. Evidently the sim- 
plest unit for such purpose is the force itself ; so the 
force existing between the earth and a gram mass is 
taken as a gravity/ unit of force and it is called a gram. 
This force when expressed in terms of the dyne is equal 
to 980 ; when expressed in terms of the gram, it is equal to 
one ; hence a force of one gram equals 980 dynes. 

Similarl}^, we may take as other units of force the force 



42 MOTION AND FOTWE [§§82-83 

of gravity existing between the earth and other units of 
mass, as the pound or the kilogram . These also are called 
gravity units of force. 

As the same names are used in this way to express both 
mass and force, care must be taken to distinguish clearly 
between them. As units of mass, the gram, pound, and 
kilogram indicate certain amounts of mass; as units of 
force, they indicate certain amounts of force. 

Of course Ave may measure other forces than gravity in 
terms of these same units. Thus a horse pulling a wagon 
may exert a force equal to 1000 pounds ; that is, a force 
which could lift a 1000-pound mass. 

83. Relation between Units. — It is frequently desirable 
to reduce certain units to other units of the same nature. 
Suppose we wish to reduce 20 pounds to grams ; we have 
only to find how many grams there are in a pound, and 
multiply by the number of pounds, or 20. Thus, according 
to the table, p. 369, to reduce pounds to grams we multi- 
ply by 453.6, or to reduce grams to pounds we multiply by 

•——--• If we wish to reduce poundals to dynes, as the 

poundal is based on the pound and the foot, and the dyne 
is based on the gram and the centimeter, we must multi- 
ply the number of poundals by the number of grams in a 
pound and then by the number of centimeters in a foot. 
We need pay no attention to the unit of time, as it is the 
same in both units of force. 



EXERCISES 

1. A bullet fired horizontally in a southerly direction from 
a building on a level plane, strikes the ground in 3 sec. If the 
initial speed is 600 ft. per sec., how far south will the bullet 
travel ? 



UNITS 43 

2. How far froia the gunner will it reach the earth if he is 
145 ft. above the ground ? 

3. A man weighing 160 lb. pushes upward on a beam with 
a force of 130 lb. What is the pressure of his feet against the 
floor ? of the beam against his hands ? of the floor against his 
feet? 

4. A boy pushes against a wall 5 ft. from the floor with a 
pressure normal to the wall of 20 lb. If his feet are 2.5 ft. 
from the wall, what force does he use ? 

5. Neglecting his weight, what is the normal pressure on 
the floor ? 

6. Three forces are acting on a body, one of 7 kg. toward 
the north, one of 11 kg. toward the east, and one of 13 kg. 
toward the south ; what is the resultant ? 

7. What would be the difference in momentum of two marbles 
rolling on the floor, one having a mass of 10 g. and a velocity of 
5 cm., the other weighing 18 g. and having a velocity of 7 cm. ? 

8. If they should strike squarely while moving in opposite 
directions, how would their velocities be affected? If their 
masses were equal, how would their velocities be affected ? 

9. What was the initial velocity of a 20-lb. cannon-ball fired 
from a 2000-lb. cannon, if the tendency of the recoil is to give 
the cannon a velocity of 15 ft. per second ? 

10. If we represent the centrifugal force by F, the mass of 
the body by m, its speed by s, and the radius of the circle in 

which it is moving by r, we have F = — ;- absolute units. 

What would be the centrifugal force of a boy whose weight 
is 100 lb. while rounding a corner on a bicycle, at a speed of 
10 mi. an hour, if the radius of the circle in which he rides is 
50 ft. ? 

11. What would be the centrifugal force acting on a boy of 
120 lb. at the equator, due to the rotation of the earth ? 

12. What would be the force at latitude 45° ? 

13. What is the force in dynes acting between the earth and 
a kilogram mass ? between the earth and a 12-lb. mass ? how 
many poundals in 100 dynes ? 



44 MOTION AND FORCE 

14. An automobile starting from rest with uniform accelerar 
tion, in 20 seconds acquires a velocity of 80 ft. in 5 seconds. 
What is its acceleration ? 

15. What would be its acceleration if the unit of velocity 
were based on the minute ? if the unit of acceleration and not 
velocity were based on the minute ? 

16. What would be its acceleration if both acceleration and 
velocity were based on the minute ? 



CHAPTER III 

GRAVITATION' 

SECTION 1. UNIVERSAL GRAVITATION 

84. Universality of Gravitation. — We have already seen 
that the force of gravitation exists between every two bodies 
in the universe. Every student of physics should have a 
clear conception of this truth. It is not difficult to realize 
that there is some force existing between the earth and a 
book lying on the desk. It requires the exercise of force 
to lift the book away from the earth ; while, if allowed to 
do so, the book will fall rapidly toward the earth without 
any assistance. 

But that there is a force existing between the book and 
the paper-weight lying near seems incredible. It appears 
as easy to move the book away from the weight as toward 
it, and there appears not the slightest tendency for the 
book to move toward the weight without assistance. 

The only difference, however, between the influence of 
the earth and that of the weight on the book is one of 
degree. The force exists between the weight and the 
book ; but just as the Aveight is extremely small compared 
with the earth, so is its influence extremely slight com- 
pared with that of the earth. If it were not for the friction 
between the book and the table, the book would move 
toward the weight and finally strike it. But the friction 
is too great to be overcome by the slight force. It is the 
same with all bodies on the surface of the earth ; there is 
always too much friction, or too much resistance of some 

45 



46 GRAVITATION [§§84-85 

kind, to allow them to move toward each other, except 
in some very special cases. And with all other bodies in 
the universe, as a rule, the force between them is not 
sufficient to overcome other forces tending to keep them 
apart. 

Yet the force exists in all cases and at all times. Not 
only every body but also every portion of matter in the 
universe is at all times attracted by this force of gravita- 
tion toward every other portion of matter. This fact is 
spoken of as the universality of gravitation. 

85. Effect of Distance on Gravitation. — So far we have 
considered gravitation only qualitatively — only with re- 
spect to its nature or quality. Now we must consider it 
quantitatively — with respect to its magnitude ; we must 
consider how its magnitude is affected by changes in the 
distance between the bodies involved and by changes in 
their masses, and also the exact magnitude of the force 
expressed in dynes. And first as to changes in distance : 

If a book or any other weight is carried to the upper 
story of a building, there is no appreciable difference in its 
weight. Yet a sensitive spring balance will indicate a 
difference ; the object will weigh less when it is taken 
farther from the earth ; and the difference is considerable 
when the object is taken to the top of a high mountain. 
This indicates that gravity decreases as the distance 
between the bodies increases — the force varies iyiversely 
with the distance. But the question at once arises, does 
it vary inversely exactly as the distance ? When the dis- 
tance is doubled, is the force halved ? 

This question was answered in 1686 by Sir Isaac Newton. 
After many years of investigation and tliought in reference 
to the matter he found that the force varies inversely as 
the square of the distance. That is, if the distance in one 
case is twice as great as in another, the force is, not one- 



§§85-88] UNIVERSAL GBAVITATION 47 

half as great, but the square of one-half, or one-fourth, as 
great. 

The method by which Newton arrived at this result is 
entirely too complicated for us to consider here. It is 
sufficient to say that it consisted in a profound investi- 
gation of the effect of the earth's attraction for the 
moon, and that of the sun for the earth and the other 
planets. 

86. Effect of Mass on Gravitation. — Every child knows 
that a large book is heavier than a small one ; that two 
quarts of water are heavier than one quart. In fact, most 
persons have a pretty well-defined notion, before studying 
physics, that the weight of any object is proportional to 
the amount of matter it contains, or to its mass. And 
physics teaches that this is strictly true. But as weight 
is the result of gravity, it is also true that gravity is 
proportional to the mass. And Newton showed also that 
it is true for gravitation as well as for gravity — the force 
between any two bodies in the universe is proportional to 
the product of their masses. 

In fact, it is to Newton that we are indebted for the com- 
plete statement of the law according to which gravitation 
acts. It was stated by him in the following form, and is 
now universally accepted as true : 

87. Law of Gravitation. — Every portion of matter in the 
universe attracts every other portion ivith a force varying 
directly as the product of the masses involved and inversely 
as the square of the distance between their centers. 

88. Discussion of the Law. — By every portion of matter 
is meant every body or portion of a body, no matter how 
large or how small. Thus the earth or any portion of it 
attracts the smallest particle of dust in the air, and even 
the individual molecules or atoms of which the dust or the 
air is composed. In fact, each molecule of the earth, sun. 



48 GBAVITATION [§§88-91 

or stars — each molecule in the universe — is supposed to 
attract every other molecule in the universe. 

The product of the masses involved means the number 
of units of mass in one of the bodies involved times the 
number of units of mass in the other. 

The square of the distance between the centers of the 
masses requires for its understanding a knowledge of what 
is meant by the center of mass of a body. 

89. Center of Mass. — As its name implies, the center of 
mass of a sphere would be the center of the sphere. It is 
that point which is nearest to all of the molecules of the 
mass, or from which the average distance to all of the mole- 
cules is as short as possible. With a straight wire it would 
be midway between the two ends and two sides of the 
wire. With a ring, however, it would not be in the mass 
of the ring at all, but in the center of the hole. 

90. Center of Gravitation. — Strictly construed, the law 
does not refer to the distance between the centers of mass 
of the masses, but the centers of gi^avitation. But as the 
center of gravitation is difScult to understand, and as it is 
practically the same as the center of mass, we will not dis- 
tinguish between them here. Strictly, the force varies 
inversely as the average of the squares of all the distances 
between every molecule of one mass and every molecule of 
the other. But for all ordinary purposes it is sufficient to 
take the square of the distances between the centers of 
mass of the bodies involved. 

91. Magnitude of Gravitation. — We will now consider 
what the actual magnitude of the force is in dynes or other 
units when the masses and their distance apart are given. 
If the magnitude of the force is known for any two given 
masses at a known distance apart, the above law enables us 
to determine the magnitude in every case where the masses 
and distance are known. 



§§91-92] UNIVERSAL GRAVITATION 49 

In 1798 Cavendish was able to measure the force existing 
between two lead balls by suspending one so that a slight 
force would cause it to move toward the other. This ex- 
periment was followed by many others of a similar nature 
during the past century, various substances being used 
for the masses under various conditions. By these ex- 
periments not only the above law was shown to be 
true, but also the magnitude of the force was accurately 
determined. 

92. Constant of Gravitation. — The force measured in 
these experiments was found to be extremely small, even 
when large masses were used. But as the force varies as 
the product of the masses, in order to determine the force 
when the masses are given, it is most convenient to know 
the force existing between unit masses. And as it varies 
inversely as the square of the distance, it is most conven- 
ient to know the force existing when the masses are unit 
distance apart. Then the force between masses of 8 g. 
each, say, will be 8 times 8, or 64, times that between masses 
of 1 g. each; and when the masses are 4 cm. apart, it 
will be one-fourth squared, or one-sixteenth, as great as 
when they are 1 cm. apart. So if we know the force 
existing between unit masses at unit distance apart, we 
can readily determine any force when the masses and dis- 
tance are known. 

In the C. G. S. system this force would be that between two 
one-gram masses with their centers of gravitation a centi- 
meter apart, and has been found to be about 0.000,000,- 
066 dyne. So in all cases this number times the product 
of the masses in grams, divided by the square of the dis- 
tance in centimeters, gives the force of gravitation in 
dynes between the masses. And it is immaterial whether 
the masses are two stars, or the earth and the moon, or 
any two bodies or portions of bodies on the surface of the 



50 GRAVITATION [§92 

earth. For this reason this number is called the constant 
of gravitation; in all determinations of gravitation it is 
the same — it is constant. It is usually indicated by Gr. 

EXERCISES 

1. How many poundals in 30 pounds ? how many grams ? 
how many dynes ? 

2. What would be the force between the earth and a mass of 
120 lb. at the sea-level, in grams ? in dynes ? 

3. What would be the force in dynes if the mass were 16,000 
mi. from the center of the earth ? if it were 16,000 mi. from 
the sea-level? 

4. Neglecting the buoyancy of the air, how much would a 
1000-lb. balloon weigh 20 mi. above the sea-level, taking the 
diameter of the earth as 7916 mi. ? 

5. How far must it rise to reduce its weight one-half ? 

6. The mass of the earth is 81.5, and its diameter 3| times 
that of the moon. How much would a 120-lb. boy weigh on the 



moon 



7. What is the force of gravitation between two canuon 
balls in contact, each weighing 12 kg., and being 14.5 cm. in 
diameter ? 

8. What is the density of the cannon balls ? 

9. What is the force in dynes between a mass of 1000 kg. 
and another of 4000 kg., if their centers are 2 m. apart? what is 
the force in pounds? 

10. As the moon revolves around the earth its centrifugal 
force holds in equilibrium the force between the earth and the 
moon. If, then, the moon were twice as far away, would its 
speed increase or decrease in order to maintain the equilib- 
rium ? (See problem 10, p. 43.) 

11. Does a mass on the surface of the earth weigh more 
when the moon is directly above it or when the earth is between 
it and the moon ? Could the difference be uoticed by lifting the 
mass with the hand? 



§93] GBAVITY 51 

12. If the mass of the moon were one-sixteenth as great as it 
is, what would be the force between it and the earth compared 
with the present force? between it and the sun? 

13. If the density of the sun were one-fourth as much as it 
is, and the distance to the earth one-eighth as much, what 
would be the force between it and the earth compared with 
the present force ? 

14. Neptune is 30 times as far from the sun as the sun is 
from the earth, and its mass is 17 times that of the earth. How 
many times greater is the force between it and the sun than 
between the earth and the sun? 

15. Also the diameter of Neptune is about 4.4 that of the 
earth. How much would a 100-lb. boy weigh on Neptune ? 

16. If the mean density of the earth is 5.55, what is the 
mean density of Neptune ? 

SECTION 2. GRAVITY 

93. Variations in Gravity. — We have already seen that 
gravity is a special case of gravitation, as it is the force of 
gravitation existing between the earth and bodies near its 
surface. Let us now consider more in detail this force with 
which we are so constantly associated. 

We have seen how centrifugal force, as the earth rotates, 
opposes gravity and causes its effect to diminish slightly as 
Ave approach the equator. This, of course, does not change 
the force actually existing between the body and the earth, 
but simply makes it less effective ; it varies its effect. 
For instance, if the earth were to stop rotating without 
changing its shape, bodies near the equator would gain in 
weight, while those near the poles would not, and many 
curious phenomena would follow. The Mississippi River 
would flow toward the north instead of the south; the 
oceans would grow shallower near the equator and deeper 
near the poles. 



52 



GRAVITATION 



[§§ 93-95 



But the force of gravity itself must vary under certain 
conditions. According to the law of gravitation, it must 
vary as the masses of the bodies involved vary. This 
is a matter of everyday observation ; the greater the 
amount of substance, the greater its weight. And accord- 
ing to the law it must also vary as the distance varies. 

94. Measurement of Mass. — We are now in a position 
to distinguish clearly between mass and weight. When a 
grocer " weighs " sugar on an ordinary beam balance, he de- 
termines the quantity of matter there is in the sugar ; that 
is, its mass. He places a known mass of metal on one 
pan of the balance and then places sugar on the other pan 
until the known mass is balanced ; that is, until there is 
just the same mass of sugar as of metal. It is true that 
the force which we call weight, existing betw^een the metal 
and the earth, equals that between the sugar and the 
earth. But as weight is an effect of gravity, and as 
gravity changes with the distance from the 
earth, the weight must change with every 
change of distance. Hence, the actual mag- 
nitude of either weight is unknoAvn, except 
approximately, while the mass is definitely de- 
termined. 

95. Measurement of Weight. — It is desirable, 
however, in many cases, to determine directly 
the weight of a body ; that is, the force existing 
between it and the earth. The apparatus used 
ordinarily for such purpose is the common 
spring balance, or dynamometer, one form of 
which is shown in Fig. 13. But where great 
accuracy is required the Jolly spring balance 
(Fig. 14) is preferable. The body to be 
weighed being suspended by the spring, the amount the 
spring is increased in length is proportional to the weight 




Fig. 



§§ 95-97] 



GRAVITY 



58 




of the body. So it is necessary only to determine wliat 
increase in length is produced by a unit force ; twice 
that increase would indicate two units 
of force, and so on. 

But we must now consider further the 
unit of force. In determining weight 
the gravity unit is usually used; that 
is, the force existing between the earth 
and a unit of mass. But as this force 
varies with the position of the mass 
with reference to the earth, in order 
to have an unchanging unit we must 
consider the mass at a certain position. 
And as the force on a unit mass at the 
sea-level at all places is practically the 
same, the unit is taken as the force ex- 
isting between the earth and unit mass 
when at the sea-level. 

Spring balances, however, are not very extensively used, 
either for approximate or accurate measurements, as ordi- 
narily it is the mass that is desired rather than the weight, 
and for this purpose the beam balances are more accurate. 

96. Laws of Weight. — For bodies above the surface of the 
earthy the lueight varies inversely as the square of the distance 
from the center of the earth. 

For bodies beloio the surface of the earthy the weight varies 
approximately as the distance from the center. 

97. Equilibrium. — Gravity acting upon bodies tends to 
move them nearer the earth. If it succeeds, we say the 
body falls ; if it does not, we say the body is in equilib- 
rium. We will consider falling bodies in the next section ; 
here let us consider the various cases of equilibrium ; that 
is, all cases where gravity alone is unable to move the 
body. 



Fig. 14. 



54 GRAVITATION [§§98-101 

98. Center of Gravity. — The center of gravity of a 
body is that point at which all of the mass of the body 
might be concentrated without changing the magnitude 
of the force of gravity or the direction in which it acts. 
For all ordinary purposes it may be considered as the 
center of mass of the body. And for convenience, instead 
of considering gravity as the sum of all the forces existing 
between every particle of the body and every particle of 
the earth, we may consider it as a single force acting 
between the center of mass of the body and of the earth. 

99. Direction of Gravity. — With this conception it is 
evident that the effect of gravity is the same as that of a 
force acting along the vertical line passing through the 
center of the earth and the center of mass of the body 
involved. When considering equilibrium, then, we may 
take as our system the earth, the body involved, and a 
force tending to draw them together which acts along a 
straight line joining the centers of mass. 

100. Stable Equilibrium. — Evidently with such a sys- 
tem the body will not fall if the vertical line of direction 

strikes within the base sup- 
porting the body, for in such 
a case the center of gravity 
of the body would be raised. 
For instance a cube has its 
^ center of gravity midway be- 

tween its opposite surfaces ; 
and, as shown in Fig. 15, this would rise as the body tips 
over. In any such case, where the center of gravity must 
rise as the body tips, the system is in stable equilihrhun. 

101. Unstable Equilibrium. — If, however, the line falls 
on the edge of the base, so that the center of gravity will not 
be raised if the body is tipped, the equilibrium is unstable^ 
or easily disturbed ; because any slight force tending to 



/ / 


f 

\ / 




§§ 101-102] 



GEA VITY 



55 



tip the body in siicli a direction as to throw the line away 
from the base will cause the body to fall, as its center will 
then move nearer the earth. Such is the case with the 
body shown in Fig. 16 ; or, 
a more decided case is that 
of any body balanced upon 
a point, such as the cone in 
Fig. 17. 

102. Neutral Equilibrium. 
— Between these two con- 
ditions of equilibrium, the 
one in which the center is 

raised and the other in which it is lowered on tipping, we 
have the case in which it is neither raised nor lowered, 
but simply moves horizontally. Such a case is that of a 
sphere or a cylinder rolled along a horizontal surface, and 
it is called neutral equilibrium. 




Fig. 16 



EXERCISES 

1. If the centrifugal force, due to the rotation of the earth, 
acting on a mass weighing 12 lb. at the equator is two-thirds 
of an ounce, what is the force of gravity in grams between 
the earth and the mass? 

2. Compare the weight of a 200-g. mass 1000 miles above 
the surface of the earth and another 1000 miles below the sur- 
face of the earth. 

3. At what distance above the surface would a mass weigh 
the same as it would if it were halfway between the surface 
and the center of the earth ? 

4. A lead ball of 30 kg. is placed with its center directly over 
the center of a mass of 3000 kg., so the centers of the masses 
are 2 m. apart. How much more will the ball weigh than if 
the other mass w^ere removed ? 

5. How far from the surface of the earth must a kilogram 
mass be removed in order that it may weigh 10 g. ? 



56 GRAVITATION [§§103-104 

6. If the force between two masses of 1 kg. each is 1 dyne, 
how far apart are their centers ? 

7. A cube resting horizontally on one side is tipped until it 
is in unstable equilibrium. How far upward has its center of 
mass been raised ? How far has its center moved ? 

8. How high must a balloon rise before its weight becomes 
three-fourths its weight on the surface of the earth ? 

SECTION 3. FALLING BODIES 

103. Acceleration of Falling Bodies. — If a body is left 
unsupported, gravity will cause it to move toward the 
earth, or, as it is usually expressed, to fall. Common ex- 
perience shows that as it falls it goes faster and faster — 
its velocity becomes greater and greater. For instance, a 
sled or wagon going freely down hill goes faster and 
faster. The velocity of a falling body then constantly in- 
creases — it is accelerated. And this is what is meant by 
the acceleration of falling bodies. 

104. Constant Acceleration of Falling Bodies. — If we ana- 
lyze that which causes the motion of a falling body, we find 
that the motion must be not only accelerated but also uni- 
formly accelerated — the body must have the same increase 
in velocity each second ; that is, a falling body must have 
constant acceleration. 

In the first place, the force of gravity acting on a body 
may be considered as uniform, because the distance the 
body ordinarily falls is extremely slight compared with 
the total distance to the center of the earth. And if the 
force is uniform^ the effect produced on the body by this 
force alone will be the same each second. But in the 
second place, inertia tends to keep the body moving uni- 
formly ; at the end of any second it will tend to keep the 
body moving uniformly with the velocity it then has. 

Hence the increase in velocity will ahva3's be due to 



§§104-10G] FALLING BODIES 57 

gravity alone ; and as the effect produced by gravity each 
second is the same, the increase in velocity each second 
will be the same, and the body will have uniform, or con- 
stant, acceleration. 

105. Effect of Mass on Falling Bodies. — We will now 
consider the actual magnitude of the acceleration which a 
falling body receives. And first as to the effect of its 
mass : 

If the mass of any body is increased, the force of gravity 
is proportionally increased ; and at first thought it seems 
as if its acceleration while falling would be proportionally 
increased. But this is not so. The force is increased, but 
that wdiich resists the force, the inertia of the body, is also 
increased. The inertia of the body resists Siuy change in 
its motion, it tends to keep its motion uniform, and the 
inertia increases exactly as the mass increases. The result 
is, increase the mass as much as we please, there will be no 
difference whatever in the acceleration of the body as it 
falls. 

Or, looking at it from another point of view, a certain 
mass will fall with a certain acceleration ; break the mass 
into two pieces, and the respective sums of the gravities 
and the inertias of the pieces will equal respectively the 
gravity and inertia of the whole. So there is no possible 
reason why the pieces should fall any slower when separate 
than when together, and they do not. 

106. Resistance of the Air. — We find, however, that 
equal masses do not fall with equal velocities if one of the 
bodies is bulkier than the other. Thus a gram of cotton 
would fall much slower than a gram of lead. But this is 
only because the air resistance is much more effective in the 
case of the cotton ; more air is displaced by it as it falls, 
and part of the force of gravity acting on it is equilibrated 
in this way. Take away the effect of the air, however, 



58 GRAVITATION [§§106-109 

and all bodies, no matter what their mass, size, shape, or 
density, would fall with the same acceleration. 

107. Experimental Proof. — Galileo was the first to show 
this experimentally. He ascended the leaning tower of 
Pisa, in Florence, and dropped simultaneously a one-pound 
shot and a ten-pound shot, and they were seen by the per- 
sons below to start and strike together. But it is not 
necessary to go to the top of the tower of Pisa ; dropping 
simultaneously from a second-story window a large and a 
small mass will show conclusively that the rates at which 
they fall are practically the same, or at least are not propor- 
tional to their masses. And similar proof is obtained by 
allowing balls of different masses to roll together down the 
same inclined plane, account being taken of friction. 

To show the effect of the air, w^e have only to allow two 
bodies such as a piece of lead and a piece of tissue paper 
to fall in a large glass tube from which the air has been 
removed ; it will be found that they fall together ; while 
with the tube filled with air a decided difference may be 
seen. 

108. Acceleration due to Gravity. — We find, then, that 
at the same place on the surface of the earth all bodies, if 
free to do so, w^ill fall with constant and equal acceleration. 
That is, every body will fall with constant acceleration 
during each second of its fall, and this acceleration will be 
the same for every other body. 

As the cause of this increase of velocity of a falling body 
is the force of gravity acting on the body, it is called the 
acceleration due to gravity. It is usually indicated by the 
letter ^, and in this work will be hereafter so indicated. 

109. Magnitude of ^r. — The magnitude of g is of great 
importance because if it is known, we know, as explained 
below, the magnitude of the force of gravity in absolute 
units existing between the earth and a unit mass of mat- 



§§109-111] FALLING BODIES 59 

ter, and if we know the mass of any body, we can at 
once determine the total force acting on it. It is also 
important in determining the shape of the earth. We 
have already seen that gravity mnst be less at the poles 
than at the equator, because at the poles centrifugal force 
is not effective. It has been estimated that the value of g 
at the poles, at sea-level, is 983.1 cm., while at the equator 
it is 978. This difference, however, is partly due to the 
fact that the radius of the earth at the poles is less than 
at the equator, so bodies there are nearer the center of the 
earth. For all points near the fortieth parallel of lati- 
tude, however, the value of g may be taken as 980 cm. 
or 32.16 ft. 

In Art. 81 it was stated that a gram equals approxi- 
mately 980 dynes. The reason for this may noAV be seen. 
The dyne will impart to a gram mass one unit of accelera- 
tion ; Avhile gravity acting on a gram mass is a force of 
one gram ; and this force Avill impart to the gram mass an 
acceleration of 980 units ; hence, it is equal to 980 dynes. 

110. Determination of g. — The determination of the con- 
stant of gravitation Cr (Art. 92) at any place answers for 
every other place, as it is entirely independent of gravity. 
But g must be determined independently for every place 
where it is used. And as it is of so much importance in 
science, we will give considerable attention to the methods 
of its determination. 

111. Freely Falling Body. — Apparently the simplest 
method of determining the value of g is by allowing a 
suitable body to fall freely and measuring the accelera- 
tion directly. It would be difficult to measure the accel- 
eration directly; but the distance the body falls and the 
time it takes may be determined, and from these the 
acceleration may be derived in the following manner : 

In case of a body falling from rest, as it has no velocity 



60 GRAVITATION [§111 

in the beginning and as its velocity increases uniformly, its 
average velocity will be one-half its iinal velocity; and 
the distance travelled will equal its average velocity times 
the time it falls. So, representing its final velocity by v, 
its acceleration by g, the time by t^ and the distance by d, 
we have 

d = ^vt. 



But V = gt. 

2d 



Hence <^ = J ^t\ ai^tl g = ^• 



Therefore, if we measure the distance the body falls, and 
the time taken, we can find at once the value of g. 

If g is known and the time given, the distance the body 
will fall may be found from the equation for d. Or, if it 
is desired to find the distance the body will fall in any 
particular second, we may derive an equation for that from 
the above, as follows : 

Let d' be the distance the body will fall during the de- 
sired second, and t the second; t will be also the total 
time to the end of that second. Then d' equals the total 
distance travelled during the time t^ minus the distance trav- 
elled up to the beginning of the t second, or minus the 
total distance travelled during the time (t—V)\ and we 
have 

There is no difficulty in measuring accurately the dis- 
tance the body falls ; but the time taken is so short that 
much care is required in its measurement. The measure- 
ment may be made, however, to Avithin .0002 sec. by 
allowing an iron ball to drop so that it breaks an electric 
current on starting and closes it on striking, the breaking 
and the closing being recorded on an instrument which 
records the time, called a chronograph. Or, instead of an 



§§111-112] 



FALLING BODIES 



61 



iron ball, a vibrating tuning-fork may be dropped so that 
a wire projecting from one of its prongs leaves a mark on 
a piece of smoked glass as it descends. This mark will 
show the vibrations of the fork; and as the time of vibra- 
tion may be readily found, the time in falling is easily 
determined with great accuracy. 

112. Inclined Plane. — Of the various devices which 
have been used to investigate this matter, perhaps the 
simplest is one used first by Galileo. Instead of using a 
freely falling body, he measured the velocity of a ball 
rolling down a slight incline — he ''diluted gravity" by 
means of an inclined plane. 

Referring to Fig. 18, a ball released at il[f will roll to A 
because of the force of gravity acting on it. But the rate 
of motion will be much 
less than that of a freely 
falling body, because only 
a small portion of gravity 
is effective. Thus letting 
MO represent the total 
force of gravity in mag- 
nitude and direction, we 
may resolve it into the 

force MN^ which tends to move the ball down the plane, 
and MP^ which is perpendicular to MN^ and tends to move 
the ball neither down nor up. So MN is the only portion 
of the total force which tends to move the ball. By geom- 
etry it will be seen that the triangles ABC and MNO are 
similar ; hence AB is to ^(7 as MO is to MN\ and we have 
only to find the ratio between the height and length of the 
plane to know the ratio between the force tending to move 
the ball down the plane and the entire force of gravity. 

By lowering the upper end of the plane the component of 
the total force which tends to move the ball may be made 




62 GRA VITA TION [§112 

SO small that the motion may be easily measured. And 
knowing the ratio between the two forces and the accel- 
eration produced by one, we can readily determine the 
acceleration which tlie other will produce. 

But in getting the value of g by this method with any 
degree of accuracy, allowance must be made for the fric- 
tion between the ball and the plane and for the force 
required to cause the ball to rotate. The former is ex- 
tremely slight with a good apparatus; but the latter is 
about two-sevenths of the entire force involved. 

By far the most accurate method of determining the 
value of g is by means of the pendulum, which we will 
consider next. 

EXERCISES 

1. If a freely falling body has an acceleration of 32 ft. 
the first second, what is the acceleration in meters the seventh 
second ? 

2. What is its velocity at the end of the first second? at 
the end of the sixteenth second ? 

3. If a ball of 24 g. is allowed to roll down an inclined 
plane the height of which is 8 ft. and length 24 ft., what is the 
magnitude of the force tending to move it along the plane ? 

4. What force acting parallel with the base of the plane 
would be required to support the ball ? 

5. Neglecting friction and the force required to rotate the 
ball, what would be the value of g if the acceleration of the 
ball were 327 cm. ? 

6. How far will a body fall freely in 8 sec. ? how far during 
the seventh second ? 

7. If a body falls freely 78.4 m. in 4 sec, what is the 
value of g ? 

8. A ball is thrown downward witli a velocity of 980 cm. 
per second. What will be its velocity at the end of 8 sec. ? 

9. If thrown upward with the velocity of 980 cm., what 
will be its velocity at the end of 8 sec. ? 



\ 



§§113-115] THE PENDULUM 63 

10. If thrown horizontally with a velocity of 2000 cm. per 
second, what will be its downward velocity in 2 sec. ? 

11. If thrown upward at an angle of 45° with a velocity of 
8 m. per second, what will be its downward velocity at the end 
of 3 sec. ? 

12. If thrown horizontally with a velocity of 10 m. per sec- 
ond from a height of 19.6 m., how far will it go horizontally ? 

SECTION 4. THE PENDULUM 

113. The Pendulum. — Every child is familiar with the 
pendulum as it swings to and fro in the clock on the 
mantel. There is, perhaps, no mechanical object more 
familiar, its motion and ticking attracting the attention 
of every one. The clock pendulum consists of the bob, 
which, is the heavy piece of metal at the lower end, and 
the rod which supports the bob. But any contrivance 
may be spoken of as a pendulum if it is free to swing to 
and fro. So every child who has swung in a swing of any 
kind has been a pendulum bob, he and the swing forming 
the pendulum. 

114. Compound Pendulum. — Although any freely swing- 
ing contrivance may be called a pendulum, yet, more 
strictly, a pendulum is a heavy piece of metal, usually 
circular, called the bob, and a rod or bar supporting the 
bob. The apparatus is free to vibrate to and fro in order 
to accomplish some purpose, such as regulating a clock or 
measuring periods of time. Such a contrivance is called 
a compound, or physical, pendulum. It is called compound 
because it is composed of two or more parts, such as the 
bob and the supporting rod, each of which has weight 
and would swing independently of each other if they were 
not fastened together. 

115. Simple Pendulum. — For many uses in physics the 
compound pendulum is not suitable, and a much simpler 



64 GllAVITATION l\ 

pendulum is used. The object is to secure a pendulum 
the mass of which is concentrated as nearly as possible at 
a single point. This point is the center of the bob. The 
supporting rod should be as light and small as is prac- 
ticable, so that its tendency to swing independently of the 
bob, and its retardation due to the air, shall be reduced 
to a minimum. 

But, while such a pendulum would be extremely simple 
compared to the ordinary compound pendulum, it would 
still be a compound pendulum, as its support would have 
some weight. If, however, we consider an imaginary 
pendulum in which the mass is all at the one point, with a 
weightless and frictionless support, we may call it a 
simple^ or mathematical^ pendulum. Simple because it is 
composed only of the bob, so far as the substance is con- 
cerned, and that is so concentrated as not to be retarded 
by the air. 

For convenience, however, in discussing the laws of 
pendulums that are to follow, we will speak of a simple 
pendulum as one composed of a heavy spherical bob sup- 
ported by as light a wire or thread as is practicable. 

116. Motion of a Pendulum. — We are not interested 
here in what starts the pendulum moving, but we are in 
what keeps it swinging back and forth after it is started. 
Most children are aware that it is the force of gravity 
which pulls the swing back when it has been pushed 
across ; but it will be well to see just how the force acts, 
and especially why the swing-board, or pendulum bob, 
swings horizontally and even upward. 

Referring to Fig. 19, when the bob is at J., gravity acts 
in the direction AB\ but it may be resolved, just as with 
the inclined plane, into two components, one, AC^ which is 
in a line with the support, and has no effect on tlie motion, 
of the bob, and the other, AD^ which is at right angles to 



§§ 116-118] 



THE PENDULUM 



Q^ 




Fig. 19. 



the support and tends to pull the bob under the point of 
suspension. This latter component will be effective until 
the point E is reached, when 
gravity will cease to be effec- 
tive ; but inertia will then 
carry the bob onward, even 
against gravity, until a point, 
A'^ is reached practically equal 
in height to A. So the only 
influences continuing the mo- ^ 
tion are gravity and the in- / 
ertia of the bob ; and if there -^^^ 
were no resistance to over- 
come these influences would 
continue the motion forever. 

117. Period of Vibration. 
— When the pendulum is 

swinging freely to and fro, it is said to be vibrating, and a 
swing from one side to the other is called a single vibra- 
tion, or briefly a vibration ; while a swing back and forth 
is called a complete vibration. The time taken for a 
single vibration is called the period of vibration^ or briefly, 
the period. 

For many reasons it is important to know how the period 
is affected by changes in the mass of the bob, the distance 
the bob swings from side to side, the length of the pendu- 
lum, or the force of gravity. There are certain laws of the 
pendulum in reference to these matters, and we will con- 
sider each separately. 

118. Effect of Mass on Period. — If the mass of a pendu- 
lum bob is greater in one case than in another, will the 
period of vibration be different ? Many children have 
answered this for themselves by noticing that a swing 
goes no faster with two persons than with one, or even 



66 



GRAVITATION 



[§§ 118-119 



with none. The empty swing goes with practically the 
same speed as the loaded swing, provided it goes the same 
distance in a vibration. And this is true in all cases ; a 
change in mass of the bob does not change the period — the 
period is independent of the material or mass of the bob. 

As the motion is due to the force of gravity, the usual 
impression is that the heavier the bob the quicker the 
vibration because the force is increased. But, as with 
falling bodies, increasing the mass not only increases the 
force but also increases the inertia which resists the force. 
119. Effect of Amplitude on Period. — One-half the dis- 
tance along the arc which the bob moves as it freely 
vibrates is called the ampliUide of the vibra- 
tion. Now it is evident that if two exactly 
similar pendulums are vibrating with the same 
amplitude their periods will be equal. But 
the question is, if the amplitude is greater in 
one case than in the other, how will the period 
be affected ? 

When a child is swinging he sometimes 
goes almost " up to the branches," and again 
he will "let the old cat die." In the former 
case the amplitude of his motion will be far 
greater than in the latter, yet it will be noticed 
that it takes about as long to swing back and 
forth in one case as in the other ; while the 
distance travelled is much less in one case, 
the speed is proportionately less. And this is 
Fig '?o ^^^® with pendulums generally ; changes in 
the amplitude, unless great, do not materially 
affect the period — the period is independent of the am- 
plitude. This is strictly true, however, only when the 
amplitude is very small and the change slight. 

This is easily shown by timing the vibrations of pendu- 



119-121] 



THE PENDULUM 



67 



lums having different amplitudes. And an analysis of the 
case shows it is probably true. For instance, in Fig. 20, 
if the amplitude AE is twice A' E, the angle A OE will be 
twice A' OE, the angle ABB will be twice A'B'B\ and 
the component of gravity AB will be about twice the com- 
ponent A'B'. The force, then, which is effective in moving 
the bob is twice as great, and we may assume, without a 
more complete analysis, that the distance travelled in the 
same time will be twice as great. 

120. Effect of Length on Period. — The length of a simple 
pendulum is the distance from the point of support to the 
center of the bob ; while the length of a 
compound pendulum is that of a simple 
pendulum having the same period. 

By tying a stone or any weight to a 
string and allowing it to swing as a pen- 
dulum, it will readily be seen that the 
period of vibration increases as the string 
is lengthened. And careful experiments 
show that the increase is as the square 
root of the length. 

A simple analysis shows that the period 
must increase as the length increases. 
Take, in Fig. 21, OA and OA' as two 
lengths : the effective forces AB and 
A'B' will be equal ; but the distance 
AE will be less than A'E'. Hence the 
time for A' to vibrate must be greater than for A. But 
to show that the increase in the time required is as the 
square root of the length would require too difficult an 
analysis for this work. 

121. Effect of g on Period. — We have seen that the con- 
tinuation of the pendulum's motion is due to gravity. We 
have now to see how changes in ^ affect the period. 




V 



68 GRAVITATION [§§121-122 

This is a rather difficult matter to show experimentally, 
as we cannot vary gravity at pleasure. It is true, by 
going up mountains we may diminish gravity ; but the 
amount of the diminution is uncertain, because it depends 
on the volume and density of the mountain as well as on 
the distance from the center of the earth. But by using 
an iron bob and placing beneath it a magnet, fairly good 
results may be obtained. The magnet, however, should be 
placed as far below the bob as is practicable, and the ampli- 
tude of vibration should be very short, so as to have the 
direction of the force between the magnet and the bob at 
all times practically parallel with the direction of gravity. 

Such experiments show that the period varies inversely 
as the square root of g. 

And an analysis indicates the same law ; the force actu- 
ating the bob being increased without increasing the inertia 
of the bob, necessarily the same distance will be travelled 
in less time. But to show the exact law by analysis is also 
beyond this work. 

122. Laws of Pendulums. — The foregoing effects may 
be briefly summarized into the following laws of the 
pendulum : 

The period of vibration of a pendulum is independent of 
the mass or the material of the hob. 

The period is practically independent of the amplitude. 

The period varies directly as the square root of the length. 

The period varies inversely as the square root of gravity. 

A simple way to keep the laws in mind is to concentrate 
them into the following form : The period is independent 
of the mass^ material^ or amplitude^ but varies directly as the 
square root of the length and inversely as the square root of 
gravity. 

A very convenient law in working problems is the con- 
verse of the one given in reference to the length, and is as 



§§122-125] THE PENDULUM 69 

follows : The lengths of pendulums are to each other as 
the squares of their periods. 

These laws will enable us to understand some peculiari- 
ties of the compound pendulum which we will now discuss. 

123. Point of Suspension. — As the words imply, the 
point of suspension of any pendulum is that point from 
which the pendulum is suspended. It is the point about 
which it is free to swing. 

124. Point of Oscillation. — If several weights suspended 
from the same string at different distances from the point 
of suspension are caused to vibrate as a pendulum, those 
nearer the point of suspension will tend to move faster 
than those farther away ; so that the nearer ones will be 
retarded by the farther ones, and the farther ones will 
be accelerated by the nearer ones. Evidently, then, if we 
had a bar of wood suspended as a pendulum, the upper 
particles would tend to accelerate the vibrations of the 
entire bar, while the lower ones would tend to retard 
them ; and it is also evident that there would be some 
particles between the upper and lower ones that would 
tend neither to accelerate nor to retard the vibrations, as 
they would tend to vibrate at the same rate as the entire 
bar. The point where these particles are located is called 
the point of oscillatioyi. 

125. Length of a Compound Pendulum. — Either of the 
pendulums just discussed would be a compound pendulum, 
and the length of the pendulum would necessarily be the 
distance from the point of suspension to the point of oscilla- 
tion. This is so because, if the particles at the point of 
oscillation were suspended from a weightless thread, the rate 
of vibration of the simple pendulum thus formed would 
be the same as that of the compound pendulum, and, from 
the law, if the periods are the same the lengths must be 
the same. 



70 GRAVITATION [§§126-129 

126. Interchangeability of the Points. — If the bar men- 
tioned above should be suspended from the point of oscilla- 
tion, it would be found that the former point of suspension 
had now become the point of oscillation ; that is, the points 
are interchangeable. This being so, in order to find the 
true length of a compound pendulum it is necessary only 
to find the point on the side of the center of mass opposite 
the point of suspension which will interchange with the 
point of suspension without changing the period. 

127. Equation of Period. — The derivation of the equa-~ 
tion which gives the period of vibration in terms of the 
length and of g is too difficult for this Avork. But letting t 
represent the period, and I the length, it may be shown both 
experimentally and mathematically that 



= W^. 



128. Seconds Pendulum. — A seconds pendulum is one 
that vibrates once a second. Evidently if the value of 
g is known, the length of such a pendulum may readily be 
found from the above equation. 

129. Measuring Time with Pendulums. — Among the 
most important uses of the pendulum is the measurement 
of time. Every one is familiar with its use in regulating 
clocks, but a few Avords in reference to its first use for that 
purpose and the Avay in which it regulates Avill not be amiss. 

Galileo, in 1583, while praying in the cathedral of Pisa, 
noticed a hanging lamp swinging after it had been lighted. 
He timed it with his pulse beats and found the periods 
were equal, or that they were isochronous, as it is called. 
He at once saw the value of the pendulum in measuring 
time, and applied it himself to pulse measurements. He 
also invented a pendulum clock. His invention, however, 
did not become generally known ; but fifteen years later 



§129] 



THE PEXDULUM 



71 




Huygens, without knowledge of Galileo's invention, pro- 
duced a similar clock ; and since that time clocks regulated 
by pendulums have been common. 

Figure 22 shows how the clock is regu- 
lated by the pendulum. The wheels of the 
clock are actuated by a coiled spring or a 
suspended weight, and are allowed to rotate 
a certain distance at each vibration of the 
pendulum. The pendulum itself is kept vi- 
brating by a slight impulse given it at each 
vibration by the wheels of the clock. The pen- 
dulum is thus kept going by the clock, but it 
regulates the speed of the clock by allowing a 
certain uniform movement at each vibration. 
As the period of the pendulum changes with 
its length, the speed of the clock may be in- 
creased by shortening the length of the pen- 
dulum, or it may be decreased by lengthening 
the pendulum. And as changes of tempera- 
ture affect the length of the pen- 
dulum rod, lengthening it when it 
becomes warmer and shortening it 
when it becomes colder, it is nec- 
essary to have a simple method of 
changing the length of the pendu- 
lum, not only to secure a proper 
period, but also to keep that pe- 
riod uniform throughout winter 
and summer. 

The pendulum is used with va- 
rious other contrivances for meas- 
uring time; for instance-, with the 
metronome (Fig. 23), which is an apparatus to beat time 
used as an assistance in studying music. 



Fig. 22. 




Fig. 23. 



72 GRAVITATION [§130 

130. Measuring g with Pendulums. — Having the equa- 
tion for the period of the pendulum in terms of its length 
and ^, in order to measure the force of gravity at any place 
it is necessary only to measure the length and period of a 
pendulum vibrating at that place. 

There is no trouble in measuring I very accurately by 
direct measurement. And, while it would be difficult to 
measure one vibration of a pendulum with much accuracy, 
yet, by measuring the time of many vibrations, hundreds 
or even thousands, and dividing the total time by the 
number of vibrations, the period may be very accurately 
determined. In fact, there is perhaps no experiment in 
science that is more accurate than the measurement of 
gravity with a pendulum in a proper manner. Of course 
with a compound pendulum the resistance of the air and 
other outside influences are apt to interfere ; but these 
must be eliminated, the influence of the air frequently 
being removed by placing the pendulum in a vacuum. 

EXERCISES 

1. If a pendulum bob weighs 24 g., what force will tend to 
vibrate the pendulum when it is moved side wise so as to form 
an angle of 45° with its normal position ? 

2. What effect would doubling its mass have on its period ? 

3. If the length of the pendulum in the above case is 50 cm., 
what is the amplitude of its first vibration ? 

4. If its length is doubled, how will its period compare with 
its original period ? 

5. How will its periods compare if it is increased in length 
from 50 to 51 cm. ? 

6. If g were 9 times as great, how would it affect the periods 
of pendulums ? 

7. What is the length of a seconds pendulum at Chicago, 
where g = 980.264 ? 



THE PENDULUM 73 

8. From the equation of the period of pendulums how can 
you tell that the mass and amplitude do not affect the time of 
vibration ? 

9. If a clock pendulum is increased 1.0404 times its original 
length, how much slower will it run ? 

10. What is the value of g if the length of a seconds pendu- 
lum is 99.39 cm. ? 

11. If a clock which has a pendulum 12 in. long loses a 
minute each day, how much should the pendulum be short- 
ened ? 

12. If a 10 in. pendulum expands .002 of its length in warm 
weather, hoAv much time per day will it lose ? 

13. If the ratio of the periods of two pendulums is 3.6, what 
is the ratio of their lengths ? 

14. An iron pendulum bob is suspended an inch above a 
magnet and is caused to vibrate with a very small amplitude. 
If the period is one-half as long as without the magnet, what is 
the ratio of the force of the magnet to that of gravity ? 



CHAPTER IV 

MECHANICS OF SOLIDS 

SECTION 1. ENERGY AND WORK 

131. Energy is the power or ability to overcome resist- 
ance or to do work. When a horse pulls a loaded cart up 
a hill, he expends energy in overcoming the resistance of 
the cart which is caused both by the inertia of the body 
and by the force of gravity which must be overcome in 
pulling the cart up the hill. 

The greater the resistance, the greater the necessary 
expenditure of energy in overcoming it. 

132. Work means the overcoming of resistance, and 
necessitates the expenditure of energy. When a force is 
applied to a body, and causes it to move through space, 
the force is said to do work. The amount of work done 
in any case depends upon the magnitude of the force and 
the distance through which it acts ; so we may represent 
the work done by the product of the numbers representing 
respectively the magnitude of the force and the distance 
through which it acts. 

133. The Foot-pound. — If a body is lifted vertically, the 
force of gravity must be overcome, and the amount of work 
done is determined by the weight of the body and the 
height to which it is raised. If one pound of matter is 
raised one foot high, a certain amount of work will be 
done. If it is raised two feet, twice as much work will 
be done. Now if five pounds are substituted for the one, 
it will readily be seen that five times as much work must 

74 



§§ 131-13G] ENERGY AND WOBK 75 

be done as in the case of the one pound. So the unit of 
work, which is called the foot-pound^ is the work done in 
raising a one-pound weight one foot against the force of 
gravity. 

The number of foot-pounds of work done in lifting any 
body is the product of the weight., in pounds, and the height., 
in feet, to which it is raised. 

The hilogr ammeter is a metric unit which is often used, 
and is the work done in raising one kilogram of matter 
one meter high against the force of gravity. 

These are the gravity units of work, as they are based 
on the force of gravity. Their magnitudes, of course, 
vary with the latitude as gravity itself varies. 

Just as the gravity units of force, these units need not be 
confined to the raising of weights. A force of one pound 
working in any direction through a distance of one foot 
would be a foot-pound. 

134. The Erg. — The erg is the C.G.S. absolute unit of 
work measure. It is the work done by a force of one dyne 
working through a distance of one centimeter. In other 
words, if a force, sufficient to give to a gram of matter 
perfectly free to move an acceleration of one centimeter 
per second, acts through one centimeter, the work done 
will be one erg. 

135. The Foot-poundal. — The foot-poundal is another 
absolute unit of work, in which the English units are used. 
It is the work' done by a force of one poundal luorking 
through a distance of one foot., or the work done by a force, 
sufficient to give to a pound mass an acceleration of one 
foot per second, when the force acts through one foot. 

136. The Horse-power. — A man carrying 50 lb. of 
brick up a ladder 20 ft. high does 1000 foot-pounds of 
work. A boy carrying 25 lb. at a time and making two 
trips will do the same amount of work ; but the rate of 



76 MECHANICS OF SOLIDS [§§ 136-137 

working is only half as great as the man's, for the boy 
requires twice as much time to perform the same amount 
of work. The rate of doing work is called power. The 
common unit of power is the horse-potver^ which is the 
poiver to do 33,000 foot-poimds of work ^^er minute., or 550 
per seco7id. 

To determine the horse-power (H.P.) of an engine or 
other source of power, multiply the number of pounds 
which it will raise by the height to which it can raise it in 
a given time, and divide thi^ product by the number of 
minutes of time, and this quotient by 33,000. 

Suppose an engine will raise a weight of 5000 lb. to a 
height of 200 ft. in 5 min. ; find its horse-power. 5000 
X 200 = 1,000,000 foot-pounds ; 1,000,000 - 5 = 200,000 
foot-pounds per minute ; 200,000 - 33,000 = ^ -{- H.P. 

137. Types of Energy. — A body may have energy, or 
the power to do work, by reason of its motion or by reason 
of its position. 
/^""^ Attach one end of a cord to a small car ; pass 

the other end around two pulleys, and attach it 
to a weight, as shown in Fig. 24, the weight 
resting on a support. Now set the car in 
motion, and its momentum will pull the weight 
up a certain distance, which will depend on 
the velocity of the car and the relative masses 
of the car and the weight. Suppose the weight 
to be one pound, and that it is raised one 

foot, it is evident that 
=Yy-J y the car had energy 

/enough, by reason of 
Yjq 94 its motion, to do one 

foot-pound of work. 
This energy of motion is called kinetic energy (K.E.). 
After the car comes to rest the weiorht will fall back, 



A 



§§137-139] ENERGY AND WORK 11 

and will draw the car back to its former position ; and in 
thus falling the weight will do just the same amount of 
work as was done in pulling it up. This being true, it will 
readily be seen that the weight, by reason of its elevated 
position, had power to do work ; and careful experiment 
has proven that, except for the effect of friction, this is 
exactly the same as the energy possessed by the car by 
reason of its motion. The energy luliich a body has by rea- 
son of its position is called potential energy (P.E.). 

138. Kinetic Energy. — Whenever a body is in motion, 
then, it has power of doing work because of its kinetic 
energy. The moving cannon ball is able to plough 
through the thick steel armor ; the blacksmith's hammer 
moulds into shape the hot iron ; the moving train will run 
for a long distance against the resistance of the air and 
the friction of the wheels, after the steam is shut off; 
a ball thrown upward will rise many feet simply because 
of the velocity imparted to it by the hand. 

A little thought will show that these effects are all the 
result of inertia ; in each case the inertia of the object 
tends to keep it moving against resistance, and thus over- 
comes resistance and performs work. By virtue of its 
velocity the inertia performs work on the ball against the 
force of gravity just the same as if the ball had been car- 
ried, instead of thrown, upward. 

139. Magnitude of Kinetic Energy. — It is important to 
be able to determine the amount of kinetic energy which 
a moving body possesses when its mass and velocity are 
known. For this purpose we wish an equation showing 
the relations among the energy, the velocity, and the mass. 
To arrive at such an equation mathematically, perhaps the 
simplest way is to consider the ball thrown upward. 

When a ball is thrown upward its kinetic energy per- 
forms work equal to its weight times the height to which it 

^0/ o o 



78 MECHANICS OF SOLIDS [§§139-140 

rises. We have then only to determine the height to which 
it will rise with a given velocity ; that is, the relation 
between height (A) and velocity (v). .-^ 

Under Falling Bodies we have the equations d = ^gt^ 

•dndv=gt. From these we have ^=-and, by substitu- 

^ . . . 

tion, d = But the distance the body falls in acquiring 

the velocity v will equal the height it will rise in losing the 
velocity v^ because the force which imparts the velocity in 
the one case is the force which takes it away in the other. 

Hence A = — ; and as work equals the weight (iv') times 

the height, we have K.E. = - — 

^^ 
This equation gives us kinetic energy in terms of the 

gravity units of work. In Art. 82 we saw that the abso- 
lute unit of force is equal to the gravity unit times 980, 
or, according to Art. 109, times g. Hence to reduce ki- 
netic energy to absolute units we need only multiply by g^ 

and we have -— ; or, as with absolute units we deal with 

mass Qui) instead of weight, — — 

140. Potential Energy. — Every body which is raised 
above the surface of the earth, or is moved in any way 
so that it tends to return to its former position, has 
potential energy. A clock weight wound up, or a tightly 
coiled clock spring, is a good example of potential energy. 
Many more, such as water above a mill-dam, a charged 
storage cell, and a lump of coal, might be given. The last 
two owe their store of energy to chemical affinity. In the 
case of the coal, it is energy which was stored up from the 
heat of the sun ages ago when the trees from which the 
coal was formed were growing ; in its present condition 
the coal needs only to be heated to the kindling tem- 



§§140-142] ENERGY AND WORK 79 

perature in the presence of oxygen, when it will burn and 
give up as kinetic energy the potential energy which it 
has stored up. 

141. Magnitude of Potential Energy. — When a body is 
raised against gravity, the work performed on the body 
will equal its weight times the height to which it is raised, 
and this is equal to the potential energy which it possesses 
by virtue of its position. For instance, careful experi- 
ments show that if a body is allowed to fall freely, 
its potential energy will impart to it suiEcient kinetic 
energy to raise it to the height from which it fell. Hence 
the potential energy of a raised body equals the product 
of its weight and its height. And in every case the poten- 
tial energy of a body equals the force required to over- 
come the restoring force while the body is being moved to 
its position, times the distance through which the force 
acts. 

142. Energy Convertible and Constant. — Suppose a ball 
is thrown upward at a certain velocity. When it starts, 
it has only kinetic energy. As it rises higher and higher 
its velocity decreases, and thus its kinetic energy decreases ; 
but as it is rising higher it is acquiring potential energy 
at the same rate that it is losing kinetic energy. When 
it has risen to half the height to which it will rise, it has 
lost one-half of its kinetic energy, which has been con- 
verted into potential energy, and at its highest point it 
has lost all its kinetic energy, and has only potential 
energy. 

The swing of a pendulum illustrates this exchange. 
When a heavy pendulum is set swinging, it will be no- 
ticed that for some time it swings through an arc which 
is nearly constant. At the extreme end of the swing it 
stops and starts in the opposite direction, and at this point 
it has only potential energy ; but as it swings toward its 



80 MECHANICS OF SOLIDS [§§142-143 

lowest point it gathers momentum, and at its lowest point 
it Las only kinetic energy, which is again changed to 
potential as it swings and rises to practically the same 
height on the other side. 

In either of these cases we see that the total amount of 
energy possessed by the body at any instant is just the 
same as at any other instant, although the form may 
change. There is a constant tendency for potential energy 
to change to kinetic, and we may suppose that at some 
time all of the potential energy in the universe may be 
changed to kinetic energy. If there were nothing to stop 
a body which is in motion, it w^ould go on moving at a 
uniform rate forever. So a pendulum, could it be sus- 
pended so that there were absolutely no resistance at the 
point of suspension, would, if the air offered no resistance, 
keep on swinging forever. 

143. Indestructibility of Energy. — From the examples 
given we see that energy can readily be changed from one 
form to another, and there are many other transformations 
which may as readily take place. We cannot, at this 
point, stop to discuss the transformation which takes place 
when the rolling ball or swinging pendulum has its motion 
stopped by reason of friction, and its energy is apparently 
lost. Yet the fact is that no energy is lost and no energy 
can he destroyed; it will always reappear somewhere in 
some form. / 

EXERCISES 



1. A baiy is moving at the rate of 80 ft. per second. If 
it weighs 75 lb., what is its K.E. in foot-poimds? in foot- 
poundals ? 

2. A cannon-ball weighing 12 lb. has a velocity of 500 ft. 
per second ; find its K.E. in foot-pomids. 

3. A car weighing 10 tons is moving along a track at the 
rate of 25 ft. per second ; find its K.E. in foot-pounds. 



ENERGY AND WORK 81 

4. A perfect sphere rests upon a level surface. If the 
sphere weighs 50 lb., how many foot-pounds of work must be 
done to give it a velocity of 30 ft. per second, neglecting its 
energy of rotation ? (Its K.E. will equal the work.) 

5. A free body weighing 50 g. has a velocity of 35 cm. per 
second. How many ergs of work was done in giving it this 
velocity ? 

6. A car of coal weighing 1200 lb. is lifted from a shaft 
200 ft. deep. How much work is done in the operation ? If 
it is done in half a minute, what must be the H.P. of the engine 
which does the work ? 

7. A gallon of water weighs about 8 lb. What must be 
the power of an engine which will pump 100,000 gal. of water 
to the height of 150 ft. in 10 hr. ? 

8. A force of how many poundals will be required to give 
a mass of 50 lb. a velocity of 30 ft. at the end of 3 sec. ? 

9. A pile driver weighing 800 lb. must be raised to the 
height of 30 ft. What power must an engine have to do this 
in 10 sec. ? 

10. A mass of 13 g. has a velocity of 50 cm. per second, 
imparted to it by a constant force which acted 3 sec. Find 
the magnitude of the force in dynes and the number of ergs 
of work done. 

11. A projectile weighing 3 lb. has a velocity of 500 ft. per 
second. Find its K.E. in foot-poundals ; in foot-pounds. 

12. A tank 60 ft. long, 20 ft. wide, and 15 ft. deep is filled 
with water. If a cubic foot of water weighs 62.5 lb., and 
the average height to which the water is to be raised is 25 ft., 
what must the H.P. of an engine be to empty the tank in 
5 hr. ? 

13. What must be the H.P. of an engine to supply 800 
houses with water if an average of 50 gal. is used in each 
house in 24 hr., and the height to which it must be pumped is 
30 ft., a gal. of water weighing 8 lb. ? 

14. How high can a 6-H.P. engine raise a weight of 4 tons 
in half a minute ? 



82 MECHANICS OF SOLIDS [§§ 144-145 

SECTION 2. MACHINES 

144. A Machine. — A machine is a contrivance for the 
application of energy to overcome resistance, or a contriv- 
ance for the transference or transformation of energy. 

The advantages obtained by the use of machines are : 

(1) The exchange of intensity of power for speed, as 
with the bic3^cle or the sewing-machine. 

(2) The exchange of speed for intensity of power, as in 
the use of a jack-screw in lifting a heavy weight. 

(3) The ability to change the direction of the force 
applied, as in hoisting a flag or drawing a bucket of 
mortar up to a second-story window by means of a fixed 
pulley, the force acting down and the weight going up. 

(4) The ability to utilize other forces than our own 
strength, as the wind, water power, steam power, etc. 

The?'e are six simple machines : the lever, the wheel and 
axle, the pulley, the inclined plane, the wedge, and the 
screw. Sometimes the wheel and axle is considered as a 
modified form of the lever, and the wedge and screw as 
modified forms of the inclined plane, which would reduce 
the number of simj)le machines to three. 

145. The Lever. — A lever is an inflexible bar, free to 
move about a fixed point called the fulcrum. It is most 
commonly used for lifting heavy weights a short distance. 

There are three classes of levers, which are determined 
by the arrangement of parts. When the weight ( W) is at 
one end, the force (P) is applied at the other, and the 
^vj«^ vy. fulcrum or support (P) is be- 

ys. ' 1 tween, we have a lever of the 

^ When the fulcrum is at one 
end, the force is applied at the other, and the weiglit is 
between, we have a lever of the second class (Fig. 26). 



w 



§ 145] MACHINES 83 

When the Aveight is at one end, the fulcrum at the other, 
and the force is applied between, we have a lever of the 
third class (Fig. 27). 

The part of the lever, PF^ between the fulcrum and the 
point of application of the force is called the force arm. 
The part WF is called the weight arm. The distance 



ZS ] 



xp ^ 



P F P I 

Fig. 26, Fig. 27. 

through which the force moves is called the force distance, 
Pi>, and the distance through which TT moves is called the 
weight distance, WD. 

Balance a light bar of wood upon a U-shaped piece of 
zinc or tin, by thrusting a small wire nail through the bar 
just, above the center -of gravity, as shown in Fig. 28. 
Now if a weight W of 50 g. is suspended at a point 8 
cm. from the fulcrum, F, and another weight F of 40 g. 
is suspended 10 cm. from jP, it will be found that the 
lever will balance. " By further experiment it may be 
determined that in all cases when a lever is in equilib- 
rium, the weight mul- 
tiplied by the length 
of the weight arm 
equals the force mul- 
tiplied by the force 
arm, or P x FF = 
W X WF. A study of Fig. 26, or better, experiment 
with the apparatus described, will readily show that if 
FF is greater than WF, P jnust move farther than TF, 
and we find that the equation F x FF = W x WF is true. 

We have, then, the following law of levers : the force 
multiplied hy the length of the force arm equals the iveight 




Fig. 28. 



84 



MECHANICS OF SOLIDS 



[§§ 145-147 




Fig. 29. 



midtiplied hy the weight arm. Or : The force times the dis- 
tance through which it moves equals the iveight times the 
distance through which it moves. 

146. Moment of Force. — The moment of a force is the 
magnitude of its tendency to produce rotary motion about 

a fixed point or axis, as in the 
case of the first-class lever mov- 
ing about its fulcrum. It equals 
the product of the numbers rep- 
resenting respectively the magni- 
tude of the force and its distance 
from the axis. When a lever is balanced, the moments 
of the forces acting upon the arms must be equal. In the 
case of bent levers, as shown in Figs. 29 and 30, the true 
length of the arms is the perpendicular distance from the 
line of direction of the force, or 
tile line in which the force acts, 
to the fulcrum, as ivF and jt?^. 

A modified form of the second- 
class lever is a bar resting upon 
two supports, one at either end, 
as shown in Fig. 31, with the 
weight upheld between them. The part of the load sup- 
ported by each support may be determined by calling the 
bar a second-class lever, and considering WF as the weight 
arm and PF as the force arm. In such case the propor- 
tion of the iveight supported hy each 
support is inversely proportional to 
the distance from the lueight to the 
point of support. Thus if W is 
80 lb., WF is 4 ft., and WP is 6 ft., .6 of the 80 lb. will 
be supported by jP, and .4 of 80 lb. by P. 
"^J 147. The Wheel and Axle. — The wheel and axle is a 
machine consisting of a wheel and a cylinder, fastened 




Fig. 30. 



s: 



^ 



Fig. 31. 



§§ 147-148] 



MACHINES 



85 




Fig. 32. 



m 



together and arranged to turn ^bout a common axis, as 

shown in Fig. 32. A modified form of a Avlieel and axle, 

called a windlass, is shown in Fig. 33. 

rtwili readily be seen that while the 

force is moving the circumference 

of the wheel, or the circumference 

of the circle described by the crank, 

the weight will move the circumfer- 
ence of the axle. We find by ex- 
periment that a given force acting 

on the wheel will support a weight 

on the axle as many times itself as 

the circumference, diameter, or radius of the wheel is 
times the corresponding dimension of 
the axle. Or : Px circ, diam.^ or M, 
of the wheel equals Wx circ,^ diam.^ or 
R^ of the axle. 

148. The Capstan. — The capstan 
'(Fig. 34) is a modified form of the 
wheel and axle, and consists of a 
spool or axle set on end. It is used 
for hoisting anchors of ships and for 

moving heavy weights. It is usually worked by bars 

or handspikes. In giving the 

dimensions of a capstan the di- 
ameter of the drum and the 

length of the handspikes are 

usually given, and the length 

is measured from the center of 

the drum, so that this length 

represents the radius of the 

force circle. The law of the 

capstan is the same as that of 

the wheel and axle, but of Fig. 34. 



6 



Fig. 3.: 




86 



MECHANICS OF SOLIDS 



[§§ 148-152 



course the force is the sum of all the forces applied to 
the bars. 

149. The Pulley. — A pulley is a wheel with a grooved 
circumference, over which runs a cord. Pulleys, or sheaves, 
as they are often called, are usually fixed in a frame or 
block by which they are suspended. 

150. The Single Fixed Pulley. — A single fixed pulley 
(Fig. 35 a) enables us to change the direction of the force 

applied, but affords no increase of 
intensity, force, or speed. P and W 
are equal and move equal distances; 
so a given force will support a 
weight equal to itself. 

151. The Single Movable Pul- 
ley. — If one end of a cord is 
fastened to a rigid support, and 
a pulley is suspended in the loop, 
as shown in Fig. 85 6, the end of 
the cord running over a fixed pul- 
ley, or the force pulling directly up, we find that the 
force must move twice as far as the weight is to be 
lifted ; and the weight is divided between the two parts 
of the supporting cord ; so that a given force Avill support 
a weight twice as great as itself. 

The movable pulley may also be considered as a second- 
class lever with the fulcrum at /, the weight suspended at 
x^ the center of the pulley, and the force applied at p. 
Applying the principle of moments we at once see that 
P is |- Tf, and must move twice as far, fp being the force 
arm and /a: the weight arm. 

152. The Block and Tackle, or the Combination of 
Pulleys. — A continuous cord may run over any number 
of pulleys which are arranged in two blocks, as shown in 
Fig. 36. Here we have two fixed and two movable pulleys. 




§§ 152-153] 



MACHINES 



87 



in each case ; but in a we have four parts of the support- 
ing cord which are connected with the block on which the 
weight hangs, and in h we have five parts of the cord sup- 
porting the weight. In a we have the end of the cord 
attached to the fixed block, and in b we ha)ve it attached 
to the movable block. Hence, when the end of the cord 

is attached to the fixed block, we have 

twice as many parts to the supporting 
cord as there are pulleys in the mov- 
able block ; but when the end is at- 
tached to the movable block, we have 
twice as many plus one. 

Experiment will show that with the 
arrangement shown in Fig. 35 a the 
force must move four times as far as 
the weight is raised, and that a given 
force will support a weight four times 
as great as itself. In the other case the 
force must move five times as far as 
the weight, and a given force will support a weight five 
times as great as itself. Hence the law : With a continu- 
ous co7'd luorking over a set of loulleys^ a given force luill 
support a weight as many times as great as itself as there are 
parts of the cord supporting the weight. 

153. The Inclined Plane. — The inclined plane is a rigid 
surface inclined to the horizontal, and is ordinarily used to 
raise heavy weights against the force of gravity. In the 
use of the inclined plane we have the force of gravity re- 
solved into two components, one parallel and one perpen- 
dicular to the surface of the plane, the force of gravity of 
course acting in a line toward the center of the earth. It 
is evident that the magnitudes of the components into 
which the force of gravity is resolved will dejDend upon 
the angle of inclination of the plane. 




Fig. 36. 



88 



MECHANICS OF SOLIDS 



[§ 153 




In Figs. 37 and 38, let MO represent the pull of grav- 
ity for a certain weight, say 20 g. at M; draw the line 

20 mm. long, and resolve this 
force into two components, 
ilfiV parallel to the surface of 
the plane AB, and MP per- 
pendicular to this surface. 
By geometry MJST : MO = 
B : AB ; then as the angle 
BAC increases the side BQ 
increases, and also the com- 
ponent MN^ as shown by 
comparing Figs. 37 and 38. If, then, the line MO, 
20 mm. long, represents a force of 20 g., the length of 
the line MN\n millimeters will represent the magnitude, 
in grams, of the force required to support the weight upon 
this incline when the force acts parallel to the surface of 
the plane. 

But we may have two other cases, one when the force 
acts parallel to the base of the plane, i.e. in a horizon- 
tal direction, and the other when the force acts parallel 
to neither the surface nor 
the base of the plane. The 
latter we need not discuss; 
but when the force acts par- 
allel to the horizontal base 
of the plane we have a reso- 
lution of the force of grav- 
ity, as shown in Fig. 39, and 
the proportion MN : MO = 
BO: AC. 

In the first case (Fig. 37) 
force distance is represented by the length of the plane, 
and weight distance by the vertical height, or the dis- 




— 'C 



§§ 153-156] 



MACHINES 



89 




tance which the weight is raised directly against the force 
of gravity while the force is moving the length of the 
plane ; or these distances paay be 
represented by any numbers hav- 
ing this ratio. In the second 
case (Fig. 39) force distance is 
the length of the horizontal base 
of the plane, and weight distance 
the vertical height, or any num- 
bers having this ratio. 

154. Laws of Inclined Planes. — 
A given force acting parallel to the surface of an inclined 
plane will support a tveight as many times itself as the 
vertical height of the plane is contained times in the length 
of the incline. Or : P x length = TF X height. 

A given force acting parallel to the horizontal base of an 
inclined plane will support a weight as many times as great 
as itself as the vertical height is contained times in the length 
of the horizontal base. Or : P x length of base = W X 
height. 

155. The Wedge. — The wedge is a modified form of the 
inclined plane, in which the force usually acts parallel to 

the base of the plane, and is applied as a blow 

from a mallet or sledge. The common form of 

the wedge (Fig. 40) is really two inclined planes, 

lying bases together. 

Fig 40 '^^^® wedge is used for lifting very heavy weights 

or splittingjogs, and its law is the same as the law 

for the inclined plane. The force multiplied hy the length 

of the wedge equals the weighty or resistance^ multiplied hy 

the thickness. 

156. The Screw. — The screw is a modified form of the 
inclined plane. It consists of a spiral inclined plane run- 
ning around a cylinder of wood or some metal, usually 



90 



MECHANICS OF SOLIDS 



[§§ I06-I57 




Fig. 41. 



iron or brass, working in a nut. The nut is a block within 
which is cut a spiral corresponding to the spiral or thread 
upon the surface of the screw (Fig. 41). 
Suppose an inclined plane upon wheels, as 
indicated in Fig. 42, and a car set upon it 
and held so that it can move freely up or 
down but not forward or back. Now if the 
plane is moved in the direction shown by 
the arrow, the car will be lifted directly up. 
Cut a piece of paper the shape of the plane 
of Fig. 42, and, laying a pencil parallel to the line BC, 
wind the paper around it and we will have a spiral incline, 
as Fig. 43. Now if the car were set 
upon this and the pencil turned, 
the car would be raised or lowered 
according to the way the pencil 
was turned. 

It will be readily seen that one 
turn of the pencil would raise the 
car the distance between the ad- 
joining turns of the spiral. With a jack-screw, Fig. 41, 
the force is applied to the end of the bar or lever FP^ 
and the screw rises the distance between the ad- 
joining turns of the thread for each complete 
circuit of the power. Then the force distance 
is the circumference of the circle described by 
P, and the weight distance is the distance be- 
tween the adjoining turns of the thread, or the 
pitch. 

157. Law of Screws. — The force multiplied by 
the circumference of the circle described by the force 
is equal to the weight multiplied by the distance between 
adjoining turns of the thread or pitch. 

Or: With a screiv a given force will support a weight as 




Fig. 42. 



Fig. 43. 




Fig. 44. 



§§ 157-158] MACHINES 91 

many times itself as the pitch is contained times in the cir- 
cumference of the circle described hy the force. 

158. Compound Machines. — Often in lifting very heavy 
weights a considerable distance, or in producing a high 
rate of speed, a combination of some of the simple machines 
is used. Such a combination is called a compound machine; 
and the fact is, that nearly all of the machines in use are 
compound machines. In Fig. 44 we have an inclined 
plane upon which rests 
a car which is to be 
drawn up the incline, or 
supported by means of 
a combination of pulleys 
having two fixed and two 
movable pulleys. The 
end of the cord is attached to the movable block, thus giv- 
ing us five parts to the cord supporting the weight. Sup- 
pose the inclined plane is 20 ft. long and 4 ft. high, and we 
wish to know what force applied at P will support the 
car upon the incline. It is evident that the force of the 
car, acting parallel to the surface of the plane, will repre- 
sent the weight which is to be supported by the block and 
tackle. If the car weighs 1000 lb., the force required 
to support it upon the plane is 200 lb., for the length 
of the plane is five times its height. Then 200 lb. repre- 
sents the weight to be supported by the block and tackle ; 
and as there are five parts to the cord the force at P 
must be one-fifth of 200, or 40 lb. Or, PD on the incline 
is 20 and WB is 4. With the block and tackle the ratio 
oiPdio Wd is 5:1, so we may call Pd 5 and Wd 1; and 
we have the equation TFx Wd x WD = P x Pd x PP; or : 
1000xlx4 = Px5x20. Similarly with all compound ma- 
chines, the continued product of the weight and its distances 
equals the continued jyroduct of the force and its distances. 



92 MECHANICS OF SOLIDS [§§159-160 

SECTION 3. FRICTION 

159. Friction. — We are familiar with the fact that when 
a piece of machinery is set in motion, or a ball is set rolling, 
or a sled is set sliding on the ice, it soon stops. It is 
evident that in each case the body meets some resistance, 
for, according to the law of inertia, a perfectly free body 
tends to continue in its existing condition of motion or 
relative rest; so a moving body, if it met no resistance, 
would keep on moving forever. We know that when 
two surfaces slide over each other there is more or less 
resistance, and that in some cases this resistance is much 
greater than in others. For example, a sled slides very 
easily upon the ice, while upon the bare ground or a board 
walk the resistance is much greater. This resistance be- 
tween surfaces which are sliding over each other is called 
sliding friction ; while the resistance which a rolling body 
meets is called rolling friction. 

160. Cause of Friction. — If two surfaces could be made 
perfectly smooth, they would slip over each other without 
friction. We know that two polished surfaces move over 
each other much more easily than rough uneven ones ; but 
absolutely smooth surfaces are impossible to obtain. There 
will always be little projections and depressions upon the 
surfaces which will, to a greater or less extent, fit into 
each other; and of course these projections must be pulled 
out of the depressions, bent down, or broken off when the 
body is set in motion. If the bodies are of the same 
material, we would naturally expect the projections and 
depressions to fit each other better than if they were of 
different material, and we find by experience that friction 
between like bodies is greater than between unlike bodies. 
So in the construction of machines we often find rapidly ro~ 
tating shafts of iron placed in brass or hardened steel boxes. 



§§ 160-162] FRICTION 93 

We find that if a block of wood is laid upon a table, 
and drawn along by means of a spring balance, the fric- 
tion is nearly proportional to the pressure ; so if we 
double the weight of the body, the force required to pull 
it will be doubled. We shall also find that the area of the 
surfaces makes little or no difference in the amount of 
force required. For example, if a block of wood is four 
inches wide and two inches thick, it will require the same 
amount of force to pull it whether it lies on its side or 
on its edge. 

161. Coefficient of Friction. — The coefficient of friction 
is the ratio between the force required to keep the body in 
motion and its weight. 

Coefficient of friction = ^ , and this value does not 

pressure 

change for given surfaces, for, as has been said, the friction 
increases as the pressure increases. If we know the co- 
efficient for two surfaces, and the pressure, we can deter- 
mine the friction, because it equals the coefficient of friction 
times the pressure. 

162. Laws of Friction. — 1. Friction is directly propor- 
tional to the pressure between the surfaces in contact. 

2. Friction is independent of the area of the surfaces in 
contact. 

3. Friction is independent of the rate of motion. 

4. Friction is greater at the beginning of motion than 
when the surfaces are in motion. 

Friction is greater between rough than between smooth 
surfaces, and thus may be diminished by polishing the 
surfaces, and also by lubricating them. The lubricant 
fills the depressions between the projections so that the 
projections and depressions cannot settle together. Rolling 
friction is much less than sliding, hence the use of ball 
bearings. 



94 MECHANICS OF SOLIDS [§163 

163. Practical Application. — It is evident that the effec- 
tive energy of any machine is tlie energy applied, minus the 
friction ; for energy cannot be created, and so the work 
done by a machine cannot be greater than the amount of 
energy applied, and must be as much less as the friction 
amounts to. So, in determining the amount of force 
required to lift a weight with a certain machine, the fric- 
tion must be added to the weight. If a weight of 1000 
lb. is to be raised with a certain machine, and the effect of 
the friction on the force amounts to one-fifth of the load, 
200 must be added to the 1000 lb., making the work to be 
done equal to that of lifting 1200 lb. instead of 1000. On 
the other hand, if the weight is simply to be supported, 
the friction will help to sustain the weight, and the force 
required will be one-fifth less than that required to sup- 
port 1000 lb. if the machine were frictionless. If, how- 
ever, the force is given, and the weight which it will raise 
is to be determined, the friction is subtracted from the 
force^ for that part of the force will be required to 
overcome the friction ; but, if the weight is simply to be 
supported, the friction will help, and the friction must be 
added, for a given force will support a weight that much 
larger than if the machine were frictionless. 

EXERCISES 

1. A lever of the first class is in equilibrium. The force 
arm is 2 ft. long, and the weight arm is 8 in. long. The force 
acting on the end of the force arm is 8 lb. Find the weight. 

2. A first-class lever is 12 in. long. A force of 5 lb. acts at 
one end, and supports a weight of 15 lb. at the other. AVliere 
must the fulcrum be placed so that the lever will be in equi- 
librium, neglecting the weight of the lever ? 

3. Two boys, A and B, are carrying a load of 50 lb., sus- 
pended from a bar 5 ft. long. The weight is suspended 



FRICTION 95 

2 ft. from A. Find what part of the weight is supported 
by each. 

4. Abeam 18 ft. long is supported at its ends A and B, and 
a weight of 800 lb. is suspended at a point 8 ft. from the end 
A. Find what part of the weight is supported by each sup- 
port. 

5. The handle of a claw-hammer is lo in. long, and the head 
of a nail is held in the claw 2i in. from the point where the 
head of the hammer rests on the board. If the resistance of 
the nail is 120 lb., what force at the end of the handle will 
be required to draw it ? 

6. A weight of 180 kg. is supported by a single movable 
pulley. Find the' force required. If the weight is raised 10 
m., how far must the force move ? 

7. Find the greatest weight which can be supported by a 
force of 40 kg. acting upon a system of pulleys, two fixed and 
two movable. 

8. With the above system, what force will be required to 
raise a weight of 400 lb., if the friction of the system amounts 
to i of the weight ? 

9. What force, acting upon the rim of a wheel 3 ft. in 
diameter, will support a weight of 300 lb., suspended from the 
axle, which is 6 in. in diameter ? 

10. The axle of a windlass is 8 in. in diameter, and is 
worked by a crank 2 ft. long. What force on the crank will 
support a weight of 150 lb. on the axle ? 

11. A capstan is worked by handspikes 3 ft. long ; the drum 
of the capstan is 8 in. in diameter. If five men are hoist- 
ing an anchor weighing 1600 lb., and friction equals \ of 
the weight, what force must be exerted by each man? If 
the anchor is to be raised 125 ft., how far must each man 
walk? 

- 12. With a system of 3 fixed and 2 movable pulleys, what 
force will be required to support a weight of 600 kg. ? 

13. A plank 10 ft. long is laid from the ground to a platform 

3 ft. high. What force, acting parallel to the surface of the 



96 MECHANICS OF SOLIDS 

plauk, will support upon the incline a barrel of syrup weighing 
250 lb. ? 

14. A car rests upon an incline which rises 1 m, in 6. If 
the car weighs 300 kg., what pressure must a man exert to 
support it upon the incline ? 

15. AVhat force acting parallel to the base of an incline 
which is 15 ft. long, and has a vertical height of G ft., Avill 
support a weight of 275 lb. ? 

16. An inclined plane is 35 ft. long, and rises 7 ft. A car 
Avhich weighs 800 lb. is to be drawn up by means of a cord 
and fixed pulley. What force at the end of the cord will 
support the car ? 

17. In the last case, if friction requires 10% of the force 
applied, what force will be required to pull the car up the 
plane, and what distance must the force move to do it ? 

18. A book press has a screw with 4 threads to the inch, and 
is worked by means of a wheel 14 in. in diameter. If fric- 
tion equals J the pressure, what pressure will be exerted by a 
force of 45 lb. applied to the rim of the wheel ? 

' 19. A jack-screw having 2 threads to the inch is used to 
raise a weight of 5 tons. If the bar which w^orks the screw is 
4 ft. long, and friction is equivalent to ^ of the load, what 
force on the end of the bar will be required to raise the 
weight ? 

20. If the coefficient of friction between a log and the ground 
is f, and the log weighs 1500 lb., what force, acting at the 
end of a bar 4 ft. long, which is attached to the drum of a 
capstan 10 in. in diameter, will be required to move the log, 
if -I- of the power is used in overcoming the friction of the 
machine ? 

21. A windlass having a 6-in. axle and a crank 15 in. long, 
is placed at the top of an inclined plane 36 ft. long, reaching 
to a window 10 ft. from the ground. What force on the 
crank will support upon the incline a car weighing 720 lb., if 
the friction of the machine uses \ of the force ? What force 
will be required to draAV the car up the incline ? 



FRICTION 97 

22. A weight of 3400 lb. is suspended by means of a block 
and tackle, having three fixed and three movable pulleys. One 
end of the cord is attached to the movable block, the other end 
is wound around the drum of a windlass, having a 10-in. drum 
and a crank 20 in. long. What force, acting upon the crank, 
will support the weight, neglecting friction? If friction is 
equivalent to \ the load, what force will be required to raise 
the weight ? 

23. A weight is being raised by a jack-screw having a pitch 
of 2 cm. How far will 7 revolutions of the screw raise the 
weight ? How far will one-tenth of a revolution raise it ? 



CHAPTER V 

MECHANICS OF FLUIDS 

SECTION 1. HYDROSTATICS 

164. Fluids. — We have already spoken of solids, liquids, 
and gases. Solids are bodies which have both elasticity of 
form and volume, and resist any attempt to change their 
shape or size ; while fluids have only elasticity of volume 
or size, and take the shape of the containing vessel with 
perfect readiness. The term fluid includes both liquids 
and gases, and the main difference between them is that 
gases tend to expand indefinitely, while liquids are 
capable of comparatively little change of volume within 
the temperature range between the freezing and boiling 
points of each liquid. A change of volume is readily 
noticeable in gases for every change of pressure or tem- 
perature ; while liquids are practically incompressible, 
and change their volume very little with change of tem- 
perature. A pressure of one atmosphere, or 14.7 lb. per 
square inch, compresses a mass of water only about 2 "ooTo 
of its original volume ; while the same pressure applied to 
a mass of air under ordinary conditions reduces its volume 
one -half. 

165. Transmission of Pressure. — We find by experi- 
ment that fluids transmit pressure in all directions at 
once. When a toy balloon is inflated with gas undeu 
pressure, it always takes an almost spherical shape, which 

98 



§§ 164-165] 



HYDBO STATICS 



99 




Fig. 45. 



shows that the pressure must be nearly equal in all direc- 
tions ; for, if it were not, the balloon would bulge out 
more in the direction of greatest pressure. 

Figure 45 represents a glass globe, attached to a tube 
in which works a piston. Around the globe is a ro^v of 
holes of equal size. Fill the apparatus 
with water, and push the piston in, and 
the water will be forced out of all the 
holes Avith equal force. This can be ac- 
counted for only by supposing that the 
molecules of water move among them- 
selves without friction. 

If, as is supposed, the molecules of no 
substance, whether solid, liquid, or gas, 
at any ordinary temperature, are in act- 
ual contact with each other, but are sep- 
arated by minute spaces which no pressure can overcome, 
the transmission of pressure can be easily understood. If 
a number of molecules are pressed down into the mass of 
liquid, it will be readily seen that, if they cannot be crowded 
into actual contact, as they approach, the other molecules 
must move out of the way, and these in turn will thrust 
others away, until finally the pressure Avill be transmitted 
to the sides of the containing vessel. 

In Fig. 46 are represented a number of molecules a, J, 

c, d^ e, /, and g. If a certain pressure be applied to a it will 

be crowded between h and c, and h will exert a pressure to 

the right, and c to the left, just equal to 

the downward pressure applied to a. Then 

c Avill be pushed between e and d^ and an 

upward and downward pressure equal to a 

will be the result. 

We are familiar with many examples of transmission of 

pressure by liquids. When a pitcher is thrust down into 

:LofC. 





©0(9 



Fig. 46. 



100 MECHANICS OF FLUIDS [§§ 165-167 

a jar of water, the downward pressure lifts the water, or 
pushes it up around the pitcher. 

166. PascaPs Law. — Pressure exerted anywhere upon the 
surface of a liquid enclosed in a vessel^ is transmitted undi- 
minished in all directions^ and acts with equal force upon all 
equal surfaces^ and at right angles to the surfaces. 

167. Experimental Proof. — The experiment suggested 
in connection with Fig. 45 sliows that pressure is trans- 
mitted in all directions, and the statement of Pascal's Law 
suggests that the pressure sustained by a surface is pro- 
portional to the area of the surface, if equal surfaces 
sustain equal pressures. Suppose we have two connected 
cylinders, as shown in Fig. 47. We are familiar with the 
fact that, if water is poured into one of them, it will rise to 

the same height in both ; and it is evi- 
dent that if we pour water into ^, and 
it rises in B^ an upward pressure is nec- 
essary to lift the water against the force 
-p^ ^r. of gravity. So the downward pressure 

of the water in A must be transmitted 
laterally through the connecting pipe, and upwardly into 
the cylinder B. We find that the relative size of the 
cylinders has nothing to do with the relative heights ; 
but, of course, if B is larger, it requires more water to 
fill the tube. If B is 10 times as large as J., it is evi- 
dent that the pressure required to push the water to the 
same height in ^ as in ^ is 10 times the weight of the water 
in A. 

Now suppose we put a tight- fitting, but frictionless, 
piston into ^, and fill the tube A to any desired height. It 
is easily seen that the piston in B will support a weight 
equal to the weight of a column of water whose sectional 
area is equal to that of B^ and whose altitude is the vertical 
distance from the piston to the top of the water column 



B 




A 


i^^T;,^^^ 


I 




:- - 



Fig. 48. 



§§167-168] HYDROSTATICS 101 

in A. For the water in B would rise to this height if the 
piston were removed. Place a certain weight upon B^ 
and fill A to such a height that the weight of the water is 
more than enough to balance the weight on B^ and the 
water in A will fall and push B up until the weight of 
water in A is to the weight of the weight on B as the 
area of A is to the sectional area of B. 

Now suppose we substitute the apparatus shown in Fig. 
48 for that in Fig. 47, and suppose the diameter of the small 
tube is 1 in. and of the large one 5 in. t^ 
Their sectional areas will be propor- I, 
tional to the squares of their diameters, | 
or in the ratio of 1 to 25. Suppose we | 
place a weight of 10 g. upon the small ^ 
piston. It will correspond to a column 
of water weighing 10 g., and would support at this same 
height in the large tube a column of water, which would 
obviously weigh 25 times as much as the small weight. 
So if this be replaced by a large weight on B, and the 
two be in equilibrium, the weight on B must be 25 times 
as great as the weight on A. 

Hence, in connected cylinders, a certain power acting 
upon a piston in the smaller tube will support a weight 
upon a piston in the larger tube, as many times itself as 
the sectional area of the larger tube is times the sectional 
area of the small tube. 

This gives us the principle of the hydraulic press and 
the hydrostatic bellows. 

168. The Hydraulic Press. — The hydraulic press repre- 
sents one of the practical applications of Pascal's Law. 
Figure 49 represents, diagrammatically, a hydrostatic or 
hydraulic press. It consists of two cylinders in which 
work two pistons greatly differing in size. The smaller 
cylinder and piston, with a valve v^ make up a force-pump, 



102 



MECHANICS OF FLUIDS 



[§§ 168-169 




Fig. 49. 



which will be studied more in detail later. The piston p 
is worked by means of a powerful second-class lever AF. 
On the up stroke of the lever the cylinder c is filled with 

water from T, and on 
the down stroke the 
valve V closes. The 
water is forced through 
the valve v'^ pushes the 
piston P up, and com- 
presses the paper or 
other material which is 
placed between the rigid 
top of the machine and 
the top of piston P. 
Suppose the lever is 
attached so that FA is 
5 times FB, and a force of 50 lb. is applied at A, then 
will a force of 250 lb. be applied to the piston p. 
Now suppose the ratio of the sectional areas of the 
pistons is 1 : 100, then will the upward pressure on P be 
100 times 250 ; or it may be determined by the proportion 
1:100=250::?:. 

169. Surface of a Liquid at Rest. — The free surface of 
a liquid acted upon by gravity is always level. As has 
been said, the molecules of a liquid move among them- 
selves without friction. When a pile of dry sand or grain 
is put on a level floor, it tends to run down and spread out 
to a certain extent, but soon reaches a point where the 
friction between the grains counteracts the tendency of 
gravity to make it spread out. Now if the element of 
friction were entirely removed, the grains would slide 
down the incline until there was absolutely no incline left, 
and the surface was perfectly level. This is what takes 
place with liquids. 



170-171] 



HYDROSTATICS 



103 



Fig. 50. 



W 



170. Liquid Pressure. — A mass of liquid exerts pressure 
by reason of its weight. 

Secure three glass tubes bent as shoAvn in Fig. 50. 
Place some mercury in the elbow at the top, as shown, and 
then lower the other ends into a deep cyl- 
inder of water, being careful to keep the 
openings at the lower ends at the same 
level. The air in the tubes will transmit 
the pressure of the water to the mercury, 
and it will be seen that the deeper the 
tubes are thrust the higher the mercury 
is pushed, indicating an increase of press- 
ure as the depth increases; also that the mercury is 
pushed to the same height in all of the tubes, although 
in a the pressure must be up, in b it must be lateral, and 
in c it must be down. These facts give rise to the follow- 
ing laws : 

1. In a giveji liquid the i^essure due to gravity is directly 
proportional to the depth. 

2. The pressure at any depth is equal in all directions. 

3. The pressure is the same at all points luhich are the 
same distance below the surface. 

171. Downward Pressure of Liquids upon the Bottoms of 
Containing Vessels. — It has been found that the pressure 
of ^ liquid upon the bottom of a containing vessel depends 
only upon the depth and density of the liquid and the area 
of the bottom, and is entirely independent of the shape 
and size of the vessel. 

Figure 51 represents a piece of apparatus designed to 
prove this. It consists of several vessels of different sizes 
and shapes, having, however, bases of equal area, and being 
supplied with a movable bottom, wdiich is held in place 
by means of a cord fastened to one end of the beam of a 
balance. Upon the other end of the beam are suspended 



104 



MECHANICS OF FLUIDS 



[§§ 171-172 




Fig. 51. 



the weights which are to hold the bottom in position. 
With the same amount of weight in the scale pan it is 
found that, when water is poured into the vessels, a, 5, and 
I c, it rises to the same 

ij^jLznznsiio) height in all before 
^ " the bottom is pushed 

off and the water 
begins to run out. 
In the tube <?, with 
straight sides, we 
can readily see that 
the downward press- 
ure is equal to the 
weight of the water 
in the tube, or a col- 
umn of water whose base is the bottom of the vessel and 
whose altitude is the depth of the water in the tube. In 
the other tubes this is not apparent, but the experiment 
proves the fact. 

We have, then, the following rule or law : The pressure 
of a liquid downward upon the bottom of the containing ves- 
sel equals the tveight of a column of the liquid whose base is 
equal to the area of the bottom pressed upon and whose alti- 
tude is the depth of the water in the vessel^ regardless of the 
shape or size of the vessel above the bottom. 

172. Liquid Pressure upon Any Submerged Surface. — 
As we go below the surface of a liquid we have found that 
the pressure increases, and that it seems to be equal in all 
directions. This is easily understood, for as we go farther 
and farther below the surface we have a greater and 
greater amount of water pressing down upon that below ; 
and as this pressure is transmitted undiminished in all 
directions no other result is possible. 

To prove that upward and downward pressure is the 



172] 



HTBBOSTATICS 



105 



same at the same depth, a good experiment is to place a 
piece of cardboard over the end of a glass tube and lower 
it into the water, as shown in Fig. 52. The upward press- 
ure will hold the cardboard in its place so that 
no water can run in. Now carefully pour water f^ 
into the tube, and it will be found that the card- 
board will not be pushed off imtil the water in 
the tube is at the same level as the water in the jar 
outside. This shows that the upward pressure 
upon the cardboard is equal to the weight of a ^^^ ^^ 
column of the water whose sectional area equals 
that of the inside of the tube, and whose altitude is the 
vertical distance from the- submerged surface to the sur- 
face of the water. 

In the case of lateral pressure upon a vertical surface, 
it is evident that the pressure upon the lower part of the 
surface is greater than that upon a similar area upon the 
upper part, for the lower edge is submerged to a greater 
depth, but the pressure at the center is the average 
between the two. 

So we have the general rule that the pressure upon any 
surface submerged in a liquid is the weight of a column of the 
liquid whose base is equal to the area of the submerged sur- 
face^ and whose altitude is the distance from the center of the 
surface to the surface of the liquid, or the average depth of 
the surface below the surface of the liquid. 

In the case of a dam which determines the depth of the 
water, the average depth of the water is one-half the 
height of the dam, or one-half the depth of the water. 



EXERCISES 

1. If a cubic foot of water weighs 62.5 lb., what will be the 
lateral pressure upon a dam 75 ft. long, which stands in 16 ft. 
of water ? 



106 MECHANICS OF FLUIDS [§173 

2. A dam 80 m. long and 12 m. high is pressed against by 
water which is level with the top. Find the lateral pressure 
in kilograms. 

3. A tank has a bottom 6 ft. square, and it is 12 ft. deep. 
If the sides are rectangular, and it is full of water, what will 
be the lateral pressure on one of the sides ? 

4. Find the lateral pressure upon a vertical water gate which 
is 4 ft. square, and is set in the bottom of a dam in 20 ft. of 
water. 

5. A cylindrical tank, 4 m. in diameter and 5 m. deep, is 
filled with water. Find the total outward pressure against its 
sides in kilograms. 

6. The pistons of a hydraulic press are respectively 1 and 
12 in. in diameter. The small piston is worked by means of a 
second-class lever 30 in. long, the piston rod being attached 6 
in. from the fulcrum. If friction takes \ of the force, what 
pressure will be exerted upon the large piston by a force of 
45 lb. on the end of the lever ? 

7. A pipe, 1 in. in diameter and 30 ft. high, is screwed into 
the head of a barrel which is 20 in. in diameter. If the pipe 
is full of water, what will be the upward pressure of the water 
on the head ? If the average diameter of the barrel is 22 in., 
what will be the total bursting pressure on the sides ? 

8. Find the total crushing power upon a cubical box, 1 ft. 
on a side, which is submerged so that the top of the box is 23 
ft. under water. 

9. A tank is 3 ft. in diameter at the top, and 4 ft. at the 
bottom. If the tank is 8 ft. deep, and is full of water, what 
will be the downward pressure on the bottom ? 

10. Find the crushing pressure upon a sphere 20 cm. in 
diameter, if it is submerged in water to the average depth of 
10 m. 

SECTION 2. BUOYANCY 

173. The Principle of Archimedes. — We are familiar 
Avitli the fact that a liquid tends to lift, or buoy up, a 
solid which is placed in it. Some solids float, and some 



§§173-175] BUOYANCY 107 

simply lose a part of their weight. Swimmers find that 
they can easily lift a stone under water which they cannot 
possibly lift out of water. A submerged stone displaces, 
or pushes aside, a certain volume of water, and this, we can 
readily see, must be a quantity equal in bulk to the sub- 
merged solid. To prove this, place a cubic centimeter of 
some solid in a vessel which is graduated in cubic centi- 
meters, and it will be found that the water will rise one 
cubic centimeter. Further experiment will show that the 
submerged solid loses weight equal to the weight of the water 
displaced. This is the Principle of Archimedes. 

174. Experimental Proof. — This principle may be proved 
in the following manner : From one end of a specific grav- 
ity balance suspend a cylindrical cup fitted with 

a plug of the same metal (usually brass), which x~~ 
exactly fills it. Weigh the two in air, and then, /\ 
having them arranged as in Fig. 53, place the ^^ 
plug P in the glass of water, and it will be seen fi 
that the balance is no longer in equilibrium, but III 
that the cup and plug have lost much weight. ^fc| 
Now fill the cup with water, and when it is Pfltj 
exactly level full equilibrium will be restored. Ym. 53. 
This shows conclusively that the submerged plug 
lost weight equal to the weight of the water which it dis- 
placed. Then : Any solid submerged iu a liquid loses 
weight equal to the iveight of its oivn bulk of the liquid. 

175. Cause of Buoyant Force. — We have found that, 
beneath the surface of a liquid, pressure is exerted, and 
that this pressure is proportional to the depth, and equal 
in all directions. Suppose a cubi-c centimeter of some solid 
is submerged so that its upper surface is 10 cm. below the 
surface of the water and parallel to it (Fig. 54). We 
may disregard the lateral pressure against the sides, as 
this has no tendency to push the cube either up or down. 



Fig. 54. 



108 MECHANICS OF FLUIDS [§§175-178 

There will be a downward pressure upon the top of the 
cube equal to the weight of a column of water with a base 
of 1 cm. 2 and an altitude of 10 cm., or 10 g. 
As the lower surface is 11 cm. deep, the upward 
pressure, according to the law, must be equal to 
4>r^; the weight of 11 cm.^ of water, or 11 g. If, then, 
^^iLJiE the cube sustains an upward pressure of 11 g. and 
a downward pressure of 10 g., it will lose 1 g. of 
its weight, or the weight of 1 cm.^ of water. 
176. Floating Bodies. — If a cube of wood be placed in 
the water, it will float instead of sinking, as did the metal 
cube in the last example. Suppose a cubic centimeter of 
dry wood weighing ^ g. is placed in the water, we shall find 
that it will sink just J cm., thus displacing J cm.^ of the 
water. In other words, it sinks until the upward pressure 
of the water equals its own weight. Hence : A floati7ig 
body displaces its own weight of the liquid in which it floats. 
This may be proved experimentally by filling a dish to 
the brim with water, and placing it in another dry dish 
which has been carefully weighed. Carefully weigh a 
body which will float, and place it with great care in the 
dish of water. The water displaced will overflow, and this 
will be found to weigh the same as the body. 



SECTION 3. SPECIFIC GRAVITY 

177. Definition of Specific Gravity. — The specific gravity 
of a substance is the ratio between its iveight and the weight 
of an equal bulk of some other substaiice taken as the standard. 

For solids and liquids, the standard used is pure water, 
at the temperature of 4° C, or 39.2° F. For gases, the 
standard is air. 

178. Specific Gravity of Solids. — To determine the spe- 
cific gravity of any body, we divide the weight of the body 



§§178-180] SPECIFIC GRAVITY 109 

by the weight of an equal volume of the standard. Sup- 
pose we have a solid which is heavier than water, and is 
not soluble. Weigh it in air, then suspend it in water 
and weigh, and, according to the principle of Archimedes, 
the difference between these two weights will be the weight 
of the water displaced. Divide the weight in air by this 
difference, and the quotient will be the specific gravity of 
the body. This we shall find corresponds exactly to the 
density of the substance. If a cubic centimeter of iron 
weighs 7.2 g., its density or its specific gravity is 7.2. 

179. Solids Lighter than Water. — If the solid of which 
the s^Decific gravity is to be determined is lighter than 
water, some other method must be used, for, of course, such 
a body will float. Suppose the body is a piece of pine. 
Secure a sinker of lead or brass heavy enough to sink 
the pine. Weigh this in air, and then in water, and then 
subtract. This gives the weight of water displaced by 
the sinker. Now tie the sinker and pine together, and 
weigh the combined mass in air and in water, and the dif- 
ference will be the weight of the water displaced by the 
combined mass ; from this subtract the weight of the 
water displaced by the sinker alone, and the result will 
be the weight displaced by the pine alone. Divide the 
weight of the pine in air by this last difference, and the 
result will be the specific gravity of the pine, which will, 
of course, be less than 1. 

180. Specific-gravity Bottle, or Flask. — The common 
method of determining the specific gravity of either solids 
or liquids is by the use of the specific-gravity bottle. For 
solids secure a wide-mouthed bottle, with a ground-glass 
stopper. Fill it with water, and press the stopper into 
position with a twisting motion, so that it will be pressed 
well into place. Put it upon the scale pan with a solid the 
specific gravity of which is to be found, and weigh the two 



110 



MECHANICS OF FLUIDS 



[§§ 180-181 




Fig. 55. 



Q 



together. Then remove the stopper, and, putting the 
weight, which may be either heavier or lighter than water, 
into the bottle, replace the stopper, always be- 
ing careful that there are no air bubbles in the 
bottle, and again weigh. The difference be- 
tween the two weights will be the weight of 
the water displaced by the solid. Divide the 
weight of the body by this difference. 

For liquids, carefully weigh the bottle, or a 
specific gravity flask shown in Fig. 55^ which 
has a capillary hole through the stopper ; then fill with 
water, and again weigh. Subtract the weight of the flask 
from this weight, to determine the weight 
of the water. Dry the flask, and fill it 
with the liquid the specific gravity of 
which is to be determined, and again 
weigh. Subtract the weight of the flask, 
and divide the weight of the liquid by 
the weight of the water. 

181. The Hydrometer. — The most com- 
mon method of determining the specific 
gravity of a liquid is by means of a hy- 
drometer (Fig. 36^. This instrument de- 
pends upon the fact that a floating body 
displaces its own weight of the liquid in 
which it floats. In a light liquid it will 
sink to a greater depth than in a heavy 
one, in order to displace its weight of the 
liquid ; and in common practice hydrom- 
eters are so graduated that one can read 
the specific gravity directly from the point 
to which it sinks. If the instrument is 
to be used for liquids heavier than water, the mark indi- 
cating the density of water is placed near the top of the 




Fig. 56. 



§§ 181-182] 



SPECIFIC GRAVITY 



111 



scale, and as it is placed in the denser liquid, it will float 
higher than in water, and the mark which appears at the 
surface of the liquid indicates the specific gravity of that 
liquid. In liquids less dense than water the instrument 
used has the mark indicating the density of water near 
the bottom of the scale. 

The principle may be made clear by a simple substitute 
for the common forms of the hydrometer. Cut a light 
pine stick exactly 1 cm. square and 10 cm. long. Bore a 
hole in one end, and put in enough lead to make it float 
upright in the water. Then plug up the hole and dip the 
stick in hot paraffine to make it impervious to water, after 
marking it off in centimeters and millimeters, beginning 
at the bottom. Now place the stick in water, and, if it 
floats to the depth of 8 cm., it weighs 8 g. If we now 
place it in some other liquid, and it floats to the depth 
of only 6 cm., we know that the liquid is heavier than 
water, and that 6 cm.^ of the liquid weighs 8 g. ; and, as 
the same bulk of water weighs 6 g., the 
specific gravity of the liquid is 8 ^ 6, or 1^. 

This form of hydrometer is called a con- 
stant-weight hydrometer. 

182. The Constant-volume Hydrometer. — 
Another form of hydrometer, which is used 
for the determination of the specific gravity 
of solids, is shown in Fig. 57. It consists 
of a hollow cylinder of copper (7, large 
enough to float a weight of 50 to T5 g., a 
small rod 7io^ a wire frame WXYZ, soldered 
to this rod at n, a basket j5, and a scale pan 
P. Place a weight, the specific gravity of 
which is to be determined, in P, and add 
sand or shot until the hydrometer sinks to a certain mark 
J., upon the rod no. Remove the weight, and add metric 




Fig. 57. 



112 MECHANICS OF FLUIDS [§§ 182-183 

weights until the hydrometer again sinks to the same 
leveL These weights will equal the weight which is to 
have its specific gravity determined. Now place the 
weight in the basket B, remove the known weights from 
P, set the hydrometer in the water, and again add known 
weights until it sinks to A. The last weights added will 
equal the weight of the water displaced by the body. 
Divide the weight of the body by the weight of the water 
displaced, and the result will be the specific gravity 
sought. 

EXERCISES 

1. A solid weighs 12 g. in air and 7.5 g. in water. What is 
its volume ? 

2. A cubic foot of wood weighs 40 lb. To what depth will 
it sink in water ? 

3. A cubic foot of wood floats with 3.5 in. out of water. 
What is its specific gravity ? 

4. A solid weighs 36 g. in air and 31 g. in water. What is 
its specific gravity ? 

5. A stone weighs 12 g. in air, 8 g. in water, and 7.2 g. in a salt 
solution. What is the specific gravity of the solution ? 

6. If the stone in Exercise 5 weighs 9 g. in kerosene, what 
is the specific gravity of the kerosene? 

7. A bottle weighs 26 g. Filled with water it weighs 58 g. 
Filled with sulphuric acid it weighs 84.88 g. Find the specific 
gravity of the sulphuric acid. 

8. A sinker weighs 30 g. in air and 25 g. in water. A piece of 
wood weighs 12 g. in air. The wood and sinker together in 
water weigh 7 g. Find the specific gravity of the wood. 

SECTION 4. MECHANICS OF GASES 

183. Weight of Air. — If a flask or hollow glass globe is 
weighed while full of air, and then the air is exhausted 
and the receptacle again weighed, it will be found that 



§§ 183-184] MECHANICS OF GASES 113 

it lias lost weight. This shows that the air it first con- 
tained has an appreciable weight. Hence, as the earth 
is surrounded by a layer of air many miles deep, it will 
readily be seen that such a quantity must have a great 
amount of weight. 

The volume of a certain mass of air varies with every 
change of temperature and pressure, and thus we can see 
that a given volume of air will have a constant weight 
only at some given temperature and pressure. A liter of 
air at a temperature of 0° C, and under a pressure equal 
to the normal pressure of the atmosphere at the sea-level, 
weighs 1.293 g. 

184. Torricelli^s Experiment. — Because of its weight 
and volume the air exerts an immense pressure upon the 
surface of the earth. And from our study of liquids we 
should expect that, if the weight of the atmosphere rests 
upon the surface of a liquid, tliis downward pressure 
would be transmitted in all directions. Suppose, then, 
that we could bring a tube, with its lower end closed, 
down through the air, and place its lower end in a dish of 
water, the tube being long enough to reach entirely above 
the atmosphere. Of course there could be no air in the 
tube, and, if the end under the water were uncovered, we 
naturally should expect the downward pressure of the air 
on the surface of the water to be transmitted up into the 
tube, and the water to rise until the weight of the 
water in the tube just balanced the pressure of the air 
upon the surface of the water. The ancients knew that, 
if the air were removed from the upper end of a tube 
while the other end was under water, the water would rise 
in the tube ; but they did not understand the reason. It 
was found that the water would rise only about 34 ft., and 
Torricelli suspected that the water was held up by the 
weight of the air. With this belief he figured that, as 



114 



MECHANICS OF FLUIDS 



[§§ 184-187 



J 



mercury is 13.6 times as heavy as water, the column of 
water supported woukl be 13.6 times as high as the mer- 
cury column which would be supported under the same 
conditions. This led him to try the experiment, which 
has come to be famous as Torricelli's experiment. He 
took a glass tube about a yard long, with one end closed, 
and filled it with mercury ; then closing the open end, he 
inverted it in a dish of mercury, and uncovered the end 
beneath. The mercury in the tube fell, as he expected, 
and came to rest at a height of about 30 in., or 76 cm. 

185. Magnitude of Atmospheric Pressure. — If the tube 
in Torricelli's experiment has a sectional area of 1 cni.^, 
the column will contain 76 cm.^ of the mercury, and as a 
cubic centimeter of mercury weighs 13.6 g., the 
mercury will weigh 1033.6 g. ; consequently, 
according to Pascal's Law, the downward press- 
ure of the air upon the surface of the mercury 
must be 1033.6 g. per square centimeter. The 
pressure of the atmosphere is not always the 
same, and the pressure given is about the maxi- 
mum ; so for practical purposes we may say 
that the atmospheric pressure is 1033 g. per 
square centimeter, or 14.7 lb. per square inch. 
186. The Barometer. — The barometer is an 
instrument to determine the pressure of the 
atmosphere. It is a tube, similar to the one 
used in Torricelli's experiment, arranged in 
permanent form, with a scale attached, so that 
the height of the mercury column may be read 
at any time (Fig. 58). Usually there is a sliding vernier 
attached, so that the height can be read to tenths of a 
millimeter, or hundredths of an inch. 

187. Practical Value of the Barometer. — The barometer 
is valuable in a practical way in measuring the height of 



Fig. 58. 



MECHANICS OF GASES 115 

mountains, heights to which balloons rise, and the atmos- 
pheric pressure under different conditions at different 
times. Owing to the differences of temperature, and to 
different amounts of moisture in the atmosphere at differ- 
ent times, the atmospheric pressure and, consequently, 
the barometric reading vary at any given place. A fall 
of the mercury column indicates a diminution of pressure, 
and the probable approach of a storm. As we go up a 
mountain, or up in a balloon, we leave a certain part of 
the atmosphere below us, diminishing the weight of the 
air which presses upon the barometer, and so get a corre- 
sponding fall of the mercury. 

In water the density would be practically the same at 
any point below the surface. Hence, if we were to carry 
a barometer a certain depth below the surface of the 
water, and only the weight of the water pressed upon 
the mercury, we would have the mercury supported at 
a certain height, and, if we Avere then to raise the instru- 
ment halfway to the surface of the water, the reading 
would be just one-half the first. Or, if we were to rise 
through the water until the barometer reading was one- 
half the first reading, we would know that we had left 
one-half of the water below us. But in the air this is 
not true, as the air is so compressible. The higher we go 
the less pressure the air sustains, and consequently the less 
its density. In fact, although the atmosphere has a depth 
of hundreds of miles, we leave nearly one-half of its mass 
below us in climbing some of the highest mountains. 

188. Measurement of Pressure. — Gas pressure is fre- 
quently measured in atmospheres. At a pressure of one 
atmosphere the barometer stands at 760 mm., and this 
means a pressure of 14.7 lb. to the square inch, or 1033 g. 
to the square centimeter. A pressure of three atmospheres 
would mean a pressure of 44.1 lb. per square inch. 



116 



MECHANICS OF FLUIDS 



[§§ 189-190 






189. The Lifting Pump. —The lifting pump (Fig. 59) 
is a contrivance for pumping or lifting water from wells 

or cisterns. It consists of a barrel or cylinder 
(7, a valve v^ and a piston P, which is hollow, 
or has a hole through it which is closed by 
another valve v' . 
^1 On the up stroke of the piston, which is air- 

*^ tight or nearly so, the weight of the air is 
lifted from the valve v^ and as the pressure of 
the air upon the surface of the water in the 
cistern is transmitted upward through the 
tube of the pump, the water lifts the valve 
V, and fills the barrel of the pump. Of 
course, if the well or cistern is deep, it may 
take several strokes of the piston to remove 
the air in the tube, which will be pushed 
up ahead of the water. On the down stroke 
of the piston v is closed, dropping back into 
its place so that no water can run back ; and 
if the pump is filled with water, it pushes its 
way up through the piston, lifting the valve v' . Upon 
the next up stroke the valve v' closes, holding the water 
above the piston, and the water is lifted and flows out of 
the spout. 

190. The Force-pump. — Often it is desirable to lift 
water, or force it, to a greater height than is possible with 
the lifting pump. The greatest possible distance between 
the surface of the water and the highest point of the pis- 
ton at which a lifting pump will work is 34 ft., and 28 or 
30 ft. is as great a distance as is practicable. 

When it is desirable to raise water a greater distance than 
this, a force-pump is used (Fig. 60). The force-pump con- 
sists of a barrel or cylinder B^ a piston P, an air-chamber 
A^ and the valves v and v' . On the up stroke of P, v' is 



Fig. 59. 



§§ 190-191] 



MECHAXICS OF GASES 



117 




closed, and the pressure being removed from v, water is 
pushed up through v^ as in the case of the lifting pump. 
On the down stroke v closes, keep- 
ing the water in B from flowing 
back into the well, and it is forced 
into A through the Yalve v' faster 
than it can flow out of the spout 
aS', so the air is compressed in the 
air-chamber A. The more power- 
ful the downward stroke of B the 
more t^he air in A will be com- 
pressed, and during the next up 
stroke of the piston, v' will close 
by reason of its own weight, the 
weight of the water in A, and the 
expansive force of the air in A 
above the water. As the water 
cannot get back into B^ the ex- 
pansion of the air in A forces it out of S in a nearly con- 
tinuous stream. If it were not for the air-chamber, of 
course, the piston could be forced down only as fast as 
the water could get out of jS ; and as soon as the pressure 
of the piston ceased, the stream of water would cease to 
flow from S. 

191. The Siphon. — The siphon (Fig. 61) is an instru- 
ment for drawing liquids from a higher to a lower level, 
over the side of the containing vessel. 
Its utility was known to the ancients, 
but the exact reason of its action was 
not known till Torricelli's experiment 
was performed. Fill a bent glass tube 
with water, and, holding the ends with 
the fingers so that the water cannot run 
Fig. 61. out, place the ends in two vessels of 



Fig. 60. 




118 MECHANICS OF FLUIDS [§191 

water, as shown in Fig. 61 (it is not necessary that the 
end C of the longer arm should be under water). Note 
that the water flows from the higher to the lower vessel 
until the water stands at the same level in both, or until 
all of the water is emptied from the higher vessel. 

We have found that water moves if there is the slight- 
est difference of pressure at different points of its sur- 
face, and of course the motion is in the direction of 
the greater force, and toAvard the lesser force. So we 
may assume that there is a greater pressure upward at A 
than at 0. Suppose the sectional area of the tube to be 
1 in. 2, and that the water in the arm AB weighs 1 lb. 
and the water in the arm BO weighs 2 lb. A pressure of 
one atmosphere rests upon the surface of each vessel, and 
this pressure of 14.7 lb. per square inch will be transmitted 
undiminished upward into each arm of the siphon. In 
tlie arm AB will be a pressure of 14.7 lb., opposed by a 
pressure of 1 lb., leaving an effective pressure of 13.7 lb. 
At C^ will be a pressure of 14.7 lb., opposed by the weight 
of the water in BC, or by a pressure of 2 lb., leaving an 
effective pressure of 12.7 lb. Then, of course, as there is a 
pressure of 13.7 lb. at A^ and a pressure of 12.7 lb. at (7, 
the water will flow from A to C ; and this will continue 
until the pressures are alike, which will be when the water 
stands at the same level in both vessels, or when all the 
water has been removed from A. 

Or, looking at it in another way, if ^^C^is filled with 
water, and BC is longer than AB^ the water in BO will be 
heavier than in AB^ and as the water in both tends to 
run down, the heavier column Avill run down, and the 
weight of the air upon the water in A will push the water 
up into that arm to fill the space left by the outflow of 
the heavier column of water. When the water comes 
to the same level in the two dishes, the weights of the 



191-192] 



MECHANICS OF GASES 



119 




Fig. 62. 



two columns will balance, and of course the flow will 
cease. 

192. The Air-pump. — The air-pump (Fig. 62) is a 
pump used to remove the air from air-tight receivers. 
It consists of a cylinder (7, a piston P, and two valves 
V and v'. i? is the receiver from which the air is to be 
removed. 

The working of the air-pump de- 
pends upon the tendency of air to 
expand indefinitely, and so to occupy 
all the space allowed it. If we place 
a small balloon, in which is a small 
quantity of air, under the receiver of 
an air-pump and remove the pressure 
of the air from it, the air in the bal- 
loon will expand and the balloon will swell out so that 
care may have to be exercised to keep it from bursting. 
We see, thus, that air expands, and expands forcibly, for it 
overcomes the elastic tendency of the balloon to collapse. 

When P (Fig- 62) is raised, the valve v' is closed on 
account of its own weight and the pressure of the outside 
air, and, as the piston is air-tight, the pressure of the air is 
removed from v, leaving in the cylinder a partial vac- 
uum. As the pressure of the air is removed from the valve 
v^ the expansive power of the air in the receiver H lifts v 
and the air rushes into O until the tension is nearly the 
same in and M. It cannot be just the same, for the 
weight of the valve must be overcome. On the down 
stroke of the piston the air in O is compressed until it has 
sufficient tension to lift v' against the pressure of the air 
outside. This process goes on until the tension of the air 
in R is no longer great enough to lift v^ or until not 
enough air is taken into C to become sufficiently com- 
pressed to raise v^ against the pressure of the atmosphere. 



120 



MECHANICS OF FLUIDS 



[§§ 192-193 



Witli such a pump it will readily be seen that a perfect 
vacuum cannot be obtained. Modern pumps, however, 
are so made that, at the beginning of the up stroke, v is 
automatically raised, and on the down stroke is closed, and 
v^ is opened. Even then the air cannot all be removed, for 
the air which goes from R to C goes by expansion, and the 
tension in M and C is always the same, so only a part of 
the remaining air can be removed at each stroke. Hence, 
while a very large portion of the air can be removed, a 
perfect vacuum is impossible. 

193. Boyle's Law. — We have found that a decrease of 
pressure increases the volume of a certain mass of air ; 
and are familiar with the fact that, with a bicycle pump, a 
large quantity of air can be forced into a 
tire, and that, when this is done, the expan- 
sive power of the air makes the tire hard. 
What we now wish to determine is the exact 
relation between the volume of the air or 
any gas and the pressure upon it. 

Figure 63 represents a piece of apparatus 
used in determining this relation. ABC is a 
glass tube, with the short arm closed and the 
long arm open. JED and FGr are scales grad- 
uated in millimeters. The long arm should 
be at least a meter long, and the long scale 
is more convenient if it is made so it can 
be moved up and down, as the mark can 
then be kept level with the surface of the 
mercury in the short arm. Place a little 
mercury in the tube, and manipulate it so that it stands, 
say, at 10 in the short arm, and at the same level in both 
arms. Then the air confined in the short arm will be 
under just one atmosphere of pressure. 

Now, suppose the mercury in the barometer stands at 76 



Fia. 63. 



§§193-194] MECHANICS OF GASES 121 

cm.; we know that the pressure of the atmosphere just 
balances the weight of this column of mercury. If, then, 
we fill the long arm with mercury, so that it stands 76 cm. 
above the level of the mercury in, the short arm, the down- 
ward pressure of this column of mercury is transmitted 
upward in the short arm, and is sustained by the air in 
(7, thus adding one atmosphere of pressure, or doubling 
the original pressure. When this is done, we find that 
the volume of the air in has been reduced to one-half 
its original volume. Now, if we add two more atmos- 
pheres of pressure, this volume will again be reduced one- 
half, for the pressure will again be doubled. 

Let us take some case between one and two atmospheres, 
say one and one-half atmospheres. This would be when the 
mercury in the long arm stands 38 cm. above the surface 
of the mercury in the short arm. Suppose the length of the 
air column in the short arm is 12 cm. when the pressure is 
one atmosphere; w^e shall find in this case that, when the 
mercury is added, the length of the column will be 8 cm. 
Now let us make a proportion representing the relations 
between the various pressures and volumes. We have in 
each case one atmosphere to start with, so in the various 
cases we have : 

(1) 1 : 2 = 6 : 12, (2) 1 : 4 = 3 : 12, or 2 : 4 = 3 : 6, (3) 
1 : 1.5 = 8 : 12, in which the first ratio of each proportion 
represents the pressures in atmospheres, and the second 
ratio represents the lengths of the column of air after and 
before the change of pressure. It will readily be seen that 
the volumes are in every case inversely proportional to the 
pressures, and this is called Boyle's Law. 

194. Reduced Pressure. — The conditions of the last ex- 
periment may be reversed in the following manner : Fill 
with mercury a large glass tube, which is closed at one 
end, to the depth of 40 or 50 cm. Close the end of a 



122 MECHANICS OF FLUIDS [§§ 104-195 

small tube about 50 cm. long, and fill it with mercury 
within 5 cm. of the top, and place it, open end down, 
in the large tube, as shown in Fig. 64. Push it down 
until the mercury in the tubes is at the same 
level, and measure the exact length of the column 

I of air in the small tube. Now lift the small tube 
until the mercury in it stands one-half the height 
of the barometer column at that time above the 
level of the mercury in the large tube. It is evi- 
dent that one-half of the weight of the atmos- 
phere will be required to support this column 
of mercury in the small tube, and that the other 
half will represent the pressure upon the air in 
the small tube. We find that, under these con- 
ditions, the volume of the air in the small tube is 
Fig. 64. j^st doubled, and the following proportion repre- 
sents the conditions : 1 : J = 10 : 5. 
The law of Boyle may be stated as follows : The volume 
of a mass of gas, temperature remaining constant, varies 
inversely as the pressure it sustains. 

This is also sometimes called Marriotte's Law, as Mar- 
riotte discovered it about the same time as did Boyle, each 
making the discovery by an entirely independent series of 
experiments. 

The following corollary of the law is frequently useful : 
The mass of a gas, volume, and temperature remaining con- 
stant, varies directly as the pressure upon it. 

195. Elastic Tension of Gases. — The elastic tension of a 
gas is the tendency of the gas to expand. It is measured 
by the pressure of the gas upon the sides of the containing 
vessel. If a wide-mouth bottle be closed with a sheet of 
thin rubber, the pressure of the air in the bottle is evi- 
dently the same per square centimeter on the glass as on 
the rubber ; and on the rubber it must equal the pressure. 



§ 195] MECHANICS OF GASES 123 

of the outside air downward. Hence the elastic force, or 
tension, in such case is equal to the atmospheric pressure, 
or to the pressure upon the gas. 

And this is true in every case : The elastic tension of a 
gas is always equals though opposite^ to the pressure upon the 
gas. 

And, in case of a confined gas : The elastic tension of the 
gas^ volume^ and temperature remaining the same, varies in- 
versely as its mass. 

EXERCISES 

1. How high will a lifting pump raise water, if it is located 
upon the side of a mountain where the barometer reading is 
71 cm. ? 

2. The barometer reads 753 mm. If it is placed under a 
receiver, and air is pumped out until the reading is 45 mm., 
what proportion of the air will be removed ? 

3. If the specific gravity of sulphuric acid is 1.8, how high 
can it be raised by means of a lifting pump when the barom- 
eter reads 750 mm. ? 

4. A 75-liter tank has oxygen forced into it to a pressure of 
125 lb. per square inch. What will be the volume of the gas 
at a pressure of 15 lb. per square inch ? 

5. An inelastic gas bag has in it 850 in.^ of air when 
elevated to a certain height in a balloon. On descending to the 
earth, where the barometer* reads 754 mm., its volume is found 
to be reduced to 575 in.^ What was the barometer reading 
at the first height ? 

6. If a globe 10 cm. in diameter has four-fifths of the air 
pumped out of it, and the barometer reads 750 mm., what will 
be the total effective crushing pressure sustained by the globe ? 

7. The normal height of a water column supported by the 
atmospheric pressure being 34 ft., it is found that, upon the side 
of a mountain, water can be raised only 28 ft. in the tube of 
a lifting pump. What is the barometer reading at that 
place ? 



124 MECHANICS OF FLUIDS 

8. A mass of air having a volume of 45 cm.^ when the ba- 
rometer reads 755 mm., is carried up the side of a mountain to 
a height where its volume is increased to 60 cm.^. What is the 
barometer reading there, and what will be the pressure per 
cubic centimeter ? 

9. The pressure upon 200 cm.^ of air is changed from 998 g. 
per square centimeter to 685. What will be the volume in the 
second case, if the temperature remains the same ? 

10. If three-quarters of the air is removed from an air-pump 
receiver, when the barometer stands at 760* mm., what will 
be the elastic tension of the remaining air in grams per square 
centimeter ? 



CHAPTER VI 

HEAT 

SECTION 1. CAUSES, SOURCES, AND NATURE OF HEAT 

196. Production of Heat. — In order to understand the 
cause and nature of heat we need first to consider how it 
is produced. The ordinary way of producing heat is by 
burning wood or coal ; but as this is an abstruse phenom- 
enon, we will consider first some simpler methods. 

197. Friction. — If a person briskly rubs his hand on his 
clothing, the hand and cloth both become warm ; in fact, 
rubbing any two substances together will warm them 
both. Numerous cases arise where heat is produced in 
this way; the axles of car wheels frequently become so 
hot as to set fire to the contents of the boxes ; and railway 
brakes sometimes ignite by the intense friction. Before 
the introduction of matches, fires were started by rubbing 
together suitably arranged pieces of wood ; and now 
matches are lighted by friction. In all such cases the 
substances are heated by overcoming the friction between 
the surfaces which come in contact. 

198. Percussion. — Heat may also be produced by per- 
cussion — striking substances together. If a piece of iron 
is hammered on an anvil, it becomes warm, and may be- 
come nearly red-hot ; a piece of wood may be ignited by 
the blows of a steam hammer, while slight percussion is 
sufficient to light detonating powder. 

Of the same nature is the agitation of liquids. If a 

125 



126 



HEAT 



[§§ 198-199 



bottle partly filled with mercury is vigorously shaken, the 
mercury will become warm, and many careful experiments 
show that any agitation of a liquid tends to warm it. 
Also, compression warms the body compressed. This 
is shown when air is pumped into a bicycle 
tire by the rise in temperature of the pump 
barrel; or it may be shown better by the use 
of the "fire syringe" (Fig. Qb). If some sub- 
stance which is very inflammable is placed in 
the bottom of the cylinder, and the piston is 
quickly pushed downward, the heat generated 
by the compression of the air will be sufficient 
to set the substance on fire. 

199. Cause of Heat. — What is the reason 
bodies are warmed by friction or percussion? 
From the kinetic theory of matter (Art. 18) it 
is evident that when two bodies are rubbed or 
struck together the motion of the molecules 
coming in contact will be increased; and the 
more they are rubbed or struck, the greater 
will be the increase of motion. When the hand 
is rubbed against a piece of cloth, the molecules 
Fig. 65. of the hand have their motion increa^sed ; at the 

same time the hand becomes warmer. 
These facts indicate that the increase of heat is due 
simply to this increase of motion of the molecules. When 
a liquid is agitated, there can be no question that the mole- 
cules have their motion increased ; and as nothing is added 
to the liquid, it seems certain that the increase of heat is 
due to a change of condition in the structure of the sub- 
stance ; and it is now generally accepted that this change 
is simply an increase in the motion of the molecules. So 
we may say the cause of heat is any process that increases 
the motion of the molecules of the heated substance. 



§§200-202] CAUSES, SOURCES, NATURE OF HEAT 127 

200. Sources of Heat. — Friction, percussion, and the 
like, as sources of lieat are extremely insignificant. There 
are various other sources — combustion, the sun, the in- 
terior of the earth, and electricity being by far the most 
important. We will consider here only the first two. 

201. Combustion is the burning of substances such as 
wood and coal. The wood or coal is composed largely of 
atoms of carbon ; these atoms when heated somewhat have 
a strong attraction for the atoms of oxygen in the air, 
and this causes the atoms of carbon and oxj^gen to rush 
together and form a new substance called carbon dioxide. 
The atoms coming together so violently have their motions 
greatly increased and correspondingly heated, just as two 
masses pounded together are heated. 

Other substances than carbon act similarly ; and in all 
cases of ordinary combustion the process is the same — a 
pounding together of the atoms of oxygen and of the sub- 
stance burning. As is well known, this is a source of an 
enormous amount of our heat, in fact, of nearly all used 
in the arts. 

202. The Sun. — The other great source of heat is the 
sun ; and it is the primary source of practically all our 
heat, because millions of years ago it caused the growth 
of the trees from which nature made our coal. 

As to the manner in which the heat is produced in the 
sun there is now little uncertainty. It is generally be- 
lieved that the heat of the sun is due to the pounding 
together of the atoms and molecules of the sun because of 
the force of gravitation between them. Just as a ball fall- 
ing and striking the earth is warmed somewhat by the 
impact, so two balls or two molecules striking together 
will be warmed. And it is supposed the molecules and 
atoms of the sun are constantly falling toward the center, 
striking other molecules ; and that the heat produced by 



128 HEAT [§§202-204 

these blows accounts for the numense heat of the sun. In 
this way the molecules gradually fall nearer the center 
of the sun, causing it to become smaller but denser ; so 
the heat of the sun may be said to be due to its con- 
traction. 

203. Nature of Heat. — From what has been said, it is 
evident that heat itself is simply the effect of the motion 
of the molecules of matter, and the greater the motion the 
hotter the substance. Now we have seen in Art. 138 that, 
whenever a body is in motion, it has energy — it has 
power to perform work. It is immaterial what the size of 
the body may be ; the earth itself, or any molecule of mat- 
ter when in motion, possesses energy by virtue of its 
motion. So the heat, which is the effect of the motion 
of molecules, is itself energy in the form of molecular ki- 
netic energy. 

This conception of heat should hereafter be constantly 
kept in mind. It may be briefly stated as follows : Heat 
is the effect of the motion of the molecules of matter; 
hence it is a form of energy, and is capable of performing 
work the same as any other form of energy. 

204. Heat and Temperature. — But we must also dis- 
tinguish clearly between heat and temperature. Heat 
represents quantity^ while temperature represents inten- 
sity. If two unequal masses of red-hot iron are plunged 
in different but equal masses of ice-cold water, the water 
containing the larger piece of iron will be heated the 
more ; although the temperatures of the two pieces of iron 
are equal, both pieces being red-hot, yet the larger piece 
gives off the more heat. The temperatures are equal, but 
the quantities of heat are different. If we take a pint and 
a quart of water at the same temperature, the quart will go 
twice as far as the pint in heating some other substance, 
because it contains twice as much heat. 



§§ 205-207] EFFECTS OF HEAT 129 

SECTION 2. EFFECTS OF HEAT 

205. Expansion. — When a bar of iron is heated, it 
increases in length ; when water is heated, its volume 
usually increases ; in fact, almost all substances increase 
in size when heated. As increase in heat increases the 
motion of the molecules, they are necessarily driven far- 
ther apart by their impacts, and the body becomes larger, 
or it expands. 

So one of the effects of heat is to expand the heated 
substance. And all bodies that expand on heating must 
necessarily contract on cooling. As one of the effects of 
this contraction, we have the cracks sometimes formed in 
ice during very cold weather ; the ice contracts as it cools, 
until it pulls apart at some weak place. 

206. Some Applications of Expansion. — The regulation 
of the temperature of rooms in many buildings depends upon 
this law of expansion applied to thermostats. When the 
air in the room becomes slightly overheated, the expansion 
of a piece of metal in the thermostat causes, by means of 
a proper apparatus, the hot-air flue to be closed, and cooler 
air to pass into the room. Carriage makers put iron wheel 
tires on while they are hot, so they will contract on cool- 
ing and firmly clasp the wheels. Machinists, in a similar 
manner, frequently " shrink " metal collars on iron bars, so 
the}^ will remain in place without being otherwise fastened. 

207. Thermometers. — But the most general and useful 
application of this law is the determination of temperatures 
by means of thermometers. The thermometer, a common 
form of which is shown in Fig. Q6, is composed of a glass 
tube, sealed at the upper end, with a bulb at the lower end 
full of mercury or alcohol. The liquid at ordinary tem- 
peratures extends part way up the tube, and the remainder 
of the tube is empty. As the liquid is heated, it expands 



130 HEAT [§§207-210 

and rises in the tube, and its height in the tube indicates 
the temperature of the liquid, which is practically the same 

fas the surrounding air. A scale is placed back of 
the tube, or on the tube itself, so the increase in 
height of the liquid may be accurately determined. 

208. Standard Temperatures. — We require stand- 
ard temperatures to which all thermometers may 
be referred, just as we require standard lengths to 
which instruments for linear measurements may be 
referred. There are two standard temperatures 
almost universally used, and they are the freezing- 
and the boiling-points of water when the pressure 
of air is at 760 mm. The height at which the mer- 
cury stands, when the thermometer is submerged 
in melting ice or snow, is marked, then the height 
at which the mercury stands when it is submerged 
in steam at 760 mm. pressure, and these points are 
called the fixed points of the thermometer. 

209. Degrees. — The two points which indicate 
the standard temperatures having been determined, 
the space on the scale between those two points is 
divided into a certain number of divisions, depend- 
ing upon the kind of thermometer that is to be 
made ; and an increase in height of the mercury of 
one division ordinarily indicates an increase in tem- 
perature of one unit, or, as it is called, one degree, 
while a decrease in height of one division indicates 
a fall in temperature of one degree. 

210. Fahrenheit Thermometers. — The Fahrenheit 
thermometer is used quite generally throughout the 
United States for other than scientific purposes. On 

^ ^^ this thermometer scale there are 180 divisions be- 

i IG. GG. 

tween the freezing- and boiling-points, so an increase 
of temperature from tlie freezing to the boiling tempera- 



§§ 210-212] 



EFFECTS OF HEAT 



131 



ture is equal to 180 degrees (180°). The freezing-point is 
numbered 32, indicating 32 degrees above a certain arbi- 
trary point called zero^ while the boiling-point is num- 
bered 212, indicating 212 degrees above zero. Above the 
boiling-point the divisions are numbered consecutively as 
far as the purposes of the thermometer require. Below 
the freezing-point the divisions are numbered consecu- 
tively down to zero, and below zero they are numbered 
— 1, — 2, and so on, as far as is required. 

211. Centigrade Thermometers. — The Centigrade ther- 
mometer is used almost universally in scientific work. In 
principle it is the same as the Fahrenheit thermometer; 
but the fixed points are marked respectively 
0° and 100° ; so there are 100 divisions be- 
tween the freezing- and the boiling-points. 
Above 100° and below 0° the divisions are 
numbered similarly to the Fahrenheit, 
Unless otherwise specified, the Centigrade 
thermometer is always referred to in this 
book. 

212. Comparison of the Fahrenheit and 
Centigrade Readings. — Figure 67 shows 
the two thermometer scales so they may 
be readily compared. As there are 180 
Fahrenheit degrees in passing from the 
freezing- to the boiling-point of water, 
while there are but 100 Centigrade de- 
grees, it is evident that these degrees 
have different values, just as the centi- 
meter and the inch have different values. 
And it is also evident that the Centigrade 
degree equals 1.8 Fahrenheit degrees. 

So if we have an increase in tempera- 
ture of a certain number of degrees Cen- fig. 67. 



132 HEAT [§§212-214 

tigrade, and wish to determine how many degrees Fahren- 
heit the increase is, we have only to multiply the number 
of degrees by 1.8, or, conversely, to divide by 1.8, if we 
wish to convert Fahrenheit into Centigrade degrees. 

Suppose, however, we wish to reduce a reading with the 
Centigrade thermometer to its corresponding Fahrenheit 
value ; for instance, if the Centigrade registers 12°, what 
would be the corresponding Fahrenheit value ? If the 
freezing-point for the Fahrenheit were 0°, the value would 
be simply 12 times 1.8, or 21.6°; but, as the freezing-point 
Fahrenheit is 32°, the value would be 32 plus 21.6, or 
53.6°. And, conversely, to reduce a Fahrenheit reading 
to Centigrade we must subtract 32 from the reading to 
reduce the freezing-point to 0°, and then divide by 1.8 
to reduce the number of degrees Fahrenheit to degrees 
Centigrade. 

213. Exceptions to Law of Expansion. — When rubber is 
heated, it contracts instead of expanding ; also some 
minerals, and at certain temperatures, some metals, con- 
tract when heated. This is probably because some other 
law in reference to the relation between the molecules is 
more effective with these substances than the law of expan- 
sion. The heat may tend to expand the substance, but, it 
may be, the force of cohesion or chemism becomes more 
effective when the substance is heated, and more than off- 
sets the expanding tendency of the heat. And all the 
substances that contract on heating expand on cooling. 
Substances that crystallize as they change from a liquid to 
a solid expand as they cool and crystallize. 

214. Contraction of Water on Heating. — The most im- 
portant exception to the law of expansion is that of water 
when near the freezing-point. If ice at the melting tem- 
perature is heated, it contracts as it melts, and the water 
continues to contract until it reaches 4° Centigrade. And 



§§214-215] EFFECTS OF HEAT 133 

of course, conversely, the water expands as it cools from 
4° until it is entirely frozen. 

Above 4° and below 0° water or ice follows the law of 
expansion by heat. 

This expansion of water on freezing is of great impor- 
tance in nature. It helps to break up rocks and to pul- 
verize the soil, by the freezing of water contained in cracks 
of the rocks and soil. It causes ice to form on top of water 
instead of at the bottom, as the expanding water is lighter, 
thus preventing our lakes and rivers from freezing more 
than a foot or two deep. 

It is, however, frequently an inconvenience when water 
expands on freezing, as all vessels containing water are 
liable to burst if the water freezes ; the vessel will invaria- 
bly burst in such a case if the water is so confined that it 
cannot otherwise expand. Thus, pipes full of water, no 
matter how strong they may be, will always burst if the 
water freezes solid within them. 

215. Change of State by Heat. — Perhaps the most im- 
portant effect of heat on substances is changing them from 
solids to liquids, or from liquids to gases ; or, as it is called 
in science, changing the state of substances. We have all 
seen ice when heated change to water, and water when 
heated change to a gas called steam. And this is a char- 
acteristic of all substances ; there are no exceptions here. 
All solids when sufficiently heated will either change to 
liquids or be decomposed into gases, and all liquids when 
sufficiently heated will change to gases. 

It is not difficult to see that this is a necessary conse- 
quence of heat. As the solid is heated, the molecules 
are driven farther and farther apart, causing the force of 
cohesion between them to weaken, until they are no longer 
attracted more toward one molecule than toward other 
neighboring molecules, and hence move readily around 



134 HEAT [§§215-219 

from one position to another, and the solid becomes a 
liquid. Then as the liquid is heated the molecules are 
driven still farther apart, the cohesion between them is 
further weakened, until a point is reached where the ten- 
dency of the molecules to bound apart, when they collide, 
is so great that cohesion is no longer able to hold them 
together, and they become independent of each other — 
the liquid becomes a gas. 

216. Fusion. — When the solid melts into liquid it is 
fused, and the process is called fusion. The change, 
however, is slow ; it is slow, first, because all substances 
soften more or less before they become entirely liquid, and 
second, because it takes much heat to cause the entire 
substance to melt, and sufficient heat cannot be applied 
quickly. 

217. Melting-point. — Nevertheless there is a certain 
temperature at which each substance melts. For instance 
ice melts at 0° C, lead at 326°, mercury at — 39°. Not only 
does the ice always begin to melt at 0°, but it all melts 
before it can be heated to any higher temperature. And 
this is true also of all substances; when heated to their 
melting-points, the^/ remain at that temperature until en- 
tirely melted^ no matter how much heat is applied. The 
temperature at which the substance begins to melt is called 
its melting -pohit. 

218. Freezing-point. — Ordinarily when water is cooled 
down to 0° it freezes ; that is, its freezing- and melting- 
points are the same. And this is so with almost all 
substances ; the melting-point of the substance is its freez- 
ing-point. As a consequence when lead, say, is at 326°, it 
will become liquid if heat is added^ or if a liquid at that 
temperature, it will become solid if heat is taken away. 

219. Crystallization. — Every one who lives in the North 
is familiar with the beautiful shapes of snowflakes, frost, 



§§219-221] EFFECTS OF HEAT 135 

and other ice crystals. If a vessel of water is exposed so 
the water is cooled uniformly throughout, the water will 
gradually turn into beautiful crystals of ice. In all these 
cases we have water freezing into ice, and this process of 
freezing or turning from a liquid into symmetrically shaped 
solids or crystals, is called crystallization. It is probably 
due to a rearrangement of the atoms in the molecules, or 
of the molecules themselves, which causes them, on cooling 
sufficiently, to cohere into symmetrical groups. Many 
other substances crystallize on solidifying, and especially 
those substances which expand on cooling. It is likely 
that the special arrangement of the molecules causes them 
to take up more room, and the substances thus expand 
on cooling, instead of following the rule of contraction. 

220. Laws of Fusion. — We may condense the foregoing 
into the following statements, with reference to the lique- 
fying of solids and solidifying of liquids, which are called 
the laws of fusion. 

Under ordinary conditions^ each substance melts at a tern- 
perature ivhich is invariable for the substance^ and it solidifies 
at the same temperature. 

The teynperature of a melting or solidifying substance 
remains constant ujitil the change is complete. 

221. Evaporation. — When a little water in a dish is 
exposed to the air it soon "dries up." Wet clothes hung 
on a line in the sunshine soon become dry. In such cases 
the water passes from a liquid to a gas, the water as a gas 
passing oft' into the air, and the process is called evapo- 
ration. This phenomenon is due to the fact that the 
molecules on the surface of the water, on colliding with 
neighboring molecules, frequently bound clear away from 
the body of the liquid, and remain in the air as a gas. In 
this way any water exposed to the air gradually evaporates, 
no matter what the temperature may be. Even if the 



136 HEAT [§§221-224 

water is frozen into ice, the process still goes on ; the sur- 
face molecules of the ice still bound away from their 
fellows into surrounding space, though the process is 
slower. And the same tendency exists with all sub- 
stances — the tendency to pass from a solid, or a liquid, 
to a gas. 

222. Effect of Substance on Evaporation. — The rate of 
evaporation is influenced by several factors, each of which 
we will now consider. In the first place evaporation varies 
with the substance evaporating. Just as substances vary 
with reference to their elasticity, density, and so forth, 
so they vary with reference to the rate at which they 
evaporate. Some substances evaporate very rapidly, while 
others, as the heavy metals, evaporate extremely slowly if 
at all. This probably is largely due to the variation in 
the force of cohesion between the molecules. 

223. Effect of Heat on Evaporation. — Although water 
evaporates at all temperatures, it is evident that heat will 
increase the rate of evaporation, because it increases the 
motion of the molecules, and hence the energy with which 
they rebound on colliding. In fact, if heated sufficiently, 
any liquid will reach a temperature where the motion of 
the molecules is so great that they cannot stay together at 
all, and the liquid boils and passes rapidly into a gas. So 
we may say, as a universal rule, that heat increases the 
rate of evaporation. 

224. Effect of Area Exposed. — So far Ave have consid- 
ered, with reference to evaporation, only the condition of 
the evaporating substance. But it is necessary to consider 
also the condition of the surrounding space. Take for 
instance a bottle full of water, tightly corked with a glass 
stopper ; it is evident there would be no evaporation, as 
the molecules could not be driven by their fellows into the 
solid glass. If the cork is removed, evaporation will take 



§§224-226] EFFECTS OF HEAT 137 

place, but only from the small surface exposed in the neck 
of the bottle. If the surface exposed is increased, evapo- 
ration will increase proportionately, as there is no reason 
why it should not be as great at one part of the surface 
as at the other. So we may say, as another rule, that 
evaporation is proportional to the surface exposed. 

225. Effect of Pressure. — The reason why the molecules 
cannot be driven into the glass in the case suggested above 
is because the glass is so dense — the molecules of glass 
drive the molecules of water 'back. Similarly the mole- 
cules of air over the exposed surface of a liquid will tend 
to drive the molecules of the liquid back, and the greater 
the density of the air the less the liquid will be able to 
evaporate. This may be strikingly shown with water ; 
when air is removed from the exposed surface by means 
of an air-pump, the water evaporates very rapidly, boiling 
at ordinary temperatures. In fact, water cannot exist as 
a liquid in a vacuum ; a piece of ice in a vacuum passes 
into a gas if warmed to the melting-point. So we may 
say that evaporation increases as the gas-pressure on the 
exposed surface decreases. 

226. Effect of Water Vapor. — If there are molecules of 
water in the air, in the vicinity of the exposed surface 
of the water, there is no reason why some of these mole- 
cules may not, on colliding with other molecules in the 
air, be driven down into the water ; and the greater the 
number of water molecules in the air, the greater the num- 
ber that will be driven into the water. Hence, although 
other molecules may still be driven off, perhaps many 
more than are added in this way, yet the resultant evap- 
oration will be less. And we may say : Evaporation 
decreases as the air becomes moister — as the amount of 
water vapor in the air increases. 

The well-knoAvn drying effect of wind is, partly, because 



138 HEAT [§§226-229 

the moist air surrounding the wet articles is driven away 
by the wind, and is rephiced by drier air. 

227. General Laws of Evaporation. — We have then the 
following laws in reference to the rate at which the evapo- 
ration takes place : 

Evaporatio7i varies with the suhsta7ice evaporating. 
It increases with the temperature of the substance. 
It is proportional to the surface exptosed. 
It increases inversely as the air pressure. 
It increases inversely as the water vapor in the surround- 
ing air. 

228. Natural Results of Evaporation. — As we have 
almost everywhere more or less water exposed to the air, 
in lakes, rivers, or smaller bodies, evaporation is going 
on. constantly ; and there results from this many natural 
phenomena which are of great importance in daily life. 
Some of these we will now consider. 

229. Results on Plants and Animals. — As plants and 
animals are composed largely of water, they are some- 
times injured by the excessive evaporation of water from 
their surfaces. All farmers are familiar with this effect 
on growing crops. The leaves of corn, on hot days, curl 
up and lose their fresh, vigorous appearance ; and if the 
drought continues long enough, the corn dies. This is 
because the loss of moisture by evaporation is greater 
than the absorption through the roots. With animals, 
although the result is similar, the injurious effects are 
usually slight, as the supply of moisture is seldom so 
greatly interfered with. But, frequently, persons living 
in heated rooms are injuriously affected by too rapid 
evaporation from the skin and mucous membranes. The 
cold air from out of doors is brought into the room and 
heated ; while the heat does not diminish the amount of 
moisture in the air, it increases evaporation, and, if mois- 



§§229-232] EFFECTS OF HEAT 139 

ture is not otherwise supplied, injurious results will fol- 
low, especially to the eyes. Air at 70° F. is capable of 
taking up four times as much moisture as at 82°, so the 
need of supplying moisture to artificially heated air is 
quite apparent. 

230. Humidity. — If evaporation is so constantly going 
on, necessarily there must be, at all times, more or less 
Avater vapor in the air. And the amount of this water 
vapor is spoken of as the humidity of the air. In local- 
ities where little water is exposed, and evaporation is 
correspondingly slight, the humidity is low. But in the 
neighborhood of large bodies of water, the humidity is 
usually high ; and it would continue increasing indefinitely 
if not interfered with. 

Speaking strictly, the amount of water vapor in the air 
is its absolute humidity ; while the ratio between its abso- 
lute humidity and the amount it is capable of containing 
is its relative humidity. By humidity we refer here to 
absolute humidity. 

231. Saturation. — We have seen, however, that evapo- 
ration decreases as the air becomes moister ; and it is evi- 
dent that if it becomes sufficiently moist, or humid, the 
resultant evaporation will cease altogether, as water 
molecules will pass from the air into the water as rapidly 
as from the water into the air. When this condition is 
reached, the air is said to be saturated — it is unable to 
hold any more moisture. The relative humidity of the air 
is then 1, or 100 per cent. 

232. Effect of Temperature on Humidity. — As heat 
increases evaporation, the temperature of the air has 
much to do with its humidity; so much so that if the 
temperature is known, the humidity of the air over water 
surfaces may be quite closely inferred. As the tempera- 
ture increases, the humidity will increase; but, at any 



140 HEAT [§§232-237 

temperature, a limit to the humidity will be reached, and 
this is the point of saturation at that temperature. Hence, 
if the temperature remains constant long enough, and suf- 
ficient water is exposed, evaporation will continue until 
the air is saturated. 

233. Condensation. — But if the temperature falls when 
the air is saturated, we have, over water surfaces, more 
water A^apor passing from the air into the water than from 
the water into the air. This is called condensation; the 
vapor condenses into a liquid. Condensation, then, is the 
passing of a substance, in the form of a vapor or a gas, 
into the form of a liquid. 

234. Dew. — But water surfaces are not necessary to 
cause condensation ; the molecules of vapor collect to- 
gether on any convenient solid, if it is sufficiently cool, 
and form drops of water. Such drops collected on the 
surfaces of leaves, blades of grass, and the like, as the 
temperature falls in the evening, are called deiv. 

235. Clouds, Fog, Mist. — Similarly, drops of water col- 
lect about particles of dust in the air, when tlie conditions 
are right, and form, according to the conditions, clouds^ 
fog^ or mist. 

236. Rain. — Clouds are thus formed in cool places in 
the air, and the small drops of water of which the clouds 
are formed fall toward the ground ; but they are turned 
into vapor again on reaching the warmer air, and the 
cloud is constantly renewed by the rising of Avarm, moist 
air. In this way, ordinarily, the cloud remains nearly 
stationary, although the drops of Avater Aviiich form it are 
constantly falling. But if the falling drops are iiot thus 
vaporized by warmer air below, they reach the earth and 
form rain. 

237. Snow, Sleet, Hail. — If the air Avliere the conden- 
sation occurs is sufficiently cool, the moisture freezes as it 



§§237-239] EFFECTS OF HEAT 141 

condenses, and forms the beautiful crystals of snow. If 
these crystals pass through clouds or mist, they receive 
films of moisture from the surrounding drops of water; 
and if this too freezes, little particles of ice are formed, 
and these give us what is called sleet. If the drops of 
water or the snowflakes are driven upward by the wind, 
far above the earth, they frequently receive large accre- 
tions of moisture, either in the higher regions or on falling, 
and form hailstones ; the hailstone, however, usually has 
for its center a great number of flakes of snow solidly 
packed together. And it is interesting to remember that 
each of these snowflakes, like every snowflake and drop of 
rain, is formed about a particle of dust. 

238. Boiling. — As water is heated it evaporates faster, 
because the increased energy of the molecules enables 
them to overcome the air pressure more readily. Finally, 
if heated sufficiently, the energy enables the water mole- 
cules to overcome the air pressure entirely, and drive the 
air away from the water surface, replacing it with water 
vapor. The water then, if more heat is added, rapidly 
passes into vapor; bubbles of vapor form beneath the 
surface and rise to the top; the water is then boiling. 
Boiling, therefore, is the rapid evaporation of water which 
occurs when heat is added to it while its temperature is 
such as to cause the elastic tension of the vapor to equal 
the air pressure. 

239. Boiling-point. — The temperature at which boiling 
occurs evidently depends on the pressure of the air ; and 
that temperature which causes boiling is spoken of as the 
boiling-point or boiling temperature^ for the particular liquid 
in question, under the particular conditions surrounding it. 
The standard boiling-point, however, is that tempera- 
ture which causes water to boil when it is at the stand- 
ard air pressure, or 760 mm. As already stated, this 



142 HEAT [§§239-240 

is one of the fixed points of the thermometer, and is 
100° C. 

Just as water freezes at the melting-point of ice, so 
steam, at the standard pressure, condenses into water at 
the boiling-point of water, if the surrounding temperature 
is any lower than 100°. 

240. Laws of Boiling. — The elastic tension of the vapor 
given off during boiling is equal to the pressure upon the 
boiling liquid. 

Under similar conditions, each liquid boils at a temperature 
ivhich is invariable for the substance ; and the substance con- 
denses at the same temperature. 

The temperature of a boiling or a condensing substance 
remains constant. Heat., however., must be added or sub- 
tracted until the change is complete. 

The boiling-point varies with the pressure. 



EXERCISES 

1. If water is warmed from 10° to 60° C, how many degrees 
F. is it warmed ? 

2. If cooled from 90° to 32° C, how many degrees F. is it 
cooled ? 

3. If ice water is heated to 60° F., how many degrees C. is 
it warmed ? 

4. A range of 320° F. is what range C. ? 

5. From - 38° F. to 78° F. is what range C. ? 

6. 76° C. is what temperature F. ? 

7. 98° F. is what temperature C. ? 

a — 90° C. is what temperature F. ? 

9. At what temperature F. does ice water, when heated, 
begin to expand ? 

10. Which is denser, water at 2° or at 4° C. ? at 1° C. or 
36° F. ? 

11. What is the melting-point of lead in F. degrees ? 



§§241-242] EFFECTS OF HEAT 143 

12. How many degrees F. is the melting-point of lead above 
that of mercury ? 

13. Under what conditions will steam remain a gas while at 
760 mm. pressure and 100° C. ? 

14. Under such pressure and temperature, when will water 
remain a liquid ? 

15. What is the elastic tension in dynes per square centi- 
meter of steam passing from boiling water, when the barometer 
indicates 750 mm. ? 

SECTION 3. TRANSFERENCE OF HEAT 

241. Conduction of Heat. — When a fire is started in a 
stove the iron of the stove becomes heated, even where not 
in contact with the fire ; the heat seems to pass through 
the iron to the outside ; and it also travels up and down 
the iron of the stove a considerable distance away from the 
fire. A short iron bar heated at one end soon becomes 
warm throughout. It is evident in such cases that the heat 
is transferred along the iron from the hotter to the cooler 
parts. This is called conduction of heat. As heat is the 
energy of the molecules due to their motions, it is evident 
that, when the molecules at one part of the iron are heated, 
they will impart some of their heat or energy to their 
neighbors ; because the increased motion of one must tend 
to increase the motion of those with which it comes in 
contact. 

242. Variation in Conduction. — Just as we find some 
substances harder than others, or more malleable, or more 
dense, so we find some much better conductors of heat 
than others. Silver and copper are extremely good con- 
ductors of heat, while wood, cloth, and paper are poor 
conductors. Generally speaking metals are good conduc- 
tors, while non-metals are poor conductors. 

The state of a substance affects greatly its conducti- 



144 HEAT [§§242-244 

bility. Most substances as solids are better conductors 
than as liquids. This is probably due to the fact that 
the molecviles of solids are more closely connected than 
those of liquids, so that the increased motion of some 
readily affects the others. But some solids are poorer 
conductors than any liquids, because their molecules are 
even less compact and uniformly associated than those 
of liquids. 

An}^ substance as a gas is a poorer conductor than as 
a solid or a liquid; and gases are nearly all poorer con- 
ductors than most solids and all liquids. This difference 
is shown by the fact that a person can remain in a room 
where the air is at 100° C. for several minutes, while water 
at about half that temperature would scald the hand in 
much less time. 

243. Applications of Conductibility. — Non-conducting 
clothing is worn in winter so that the heat of the body 
will not pass away too freely. Houses are made with hol- 
low walls, so as to retain the heat in the houses in winter, 
and keep out the heat of the outer air in summer. Hot- 
water and steam pipes are covered with non-conducting 
substances ; and boilers and fireplaces are surrounded with 
bricks, which are poor conductors. 

244. Convection. — Although water will not readily 
conduct heat, every one is familiar with the fact that, 
when a vessel full of water is placed over a fire, the water 
soon becomes heated throughout. This, however, is not 
because the heat is conducted from the bottom upward, 
but because, as the lower portion is heated, it expands, 
becomes lighter, and is crowded upward by the heavier 
liquid above. If water containing some particles of saw- 
dust is heated in a glass beaker, the upper particles will be 
seen to sink at the sides of the beaker, while those directly 
over the burner will rise. Currents will tlius be set up 



§§244-246] TRANSFERENCE OF HEAT 145 

in the water which tend to keep the temperature of the 
water uniform throughout, the heat applied at the lower 
part thus being transferred to the top. This method of 
transferring heat is called convection^ and the currents set 
up are called convection currents. 

It is impossible, of course, to set up convection currents 
in solids because of their rigidity ; but gases transfer heat 
in this manner even more readily than liquids ; and this 
method of transference is far more rapid than conduc- 
tion with the best conductors. 

245. Natural Effects of Convection. — There are many 
effects of convection in nature, several of which are of the 
greatest importance. Some of these we will now consider. 

246. Wind. — When the sun rises in the morning, it 
begins to warm the air through which it shines. The 
heated air expands, thus becoming lighter, and is crowded 
upward by heavier surrounding air. As the sun shines 
with more intensity near the equator than elsewhere, there 
is a constant tendency for currents of air on the surface 
of the earth to move toward the equator, while upper cur- 
rents of warm air move toward the poles ; at the same 
time many minor currents are set up, because of the ro- 
tation of the earth, and because the passage of clouds 
between the sun and the earth constantly changes the 
intensity with which the sun shines on any particular 
place. All such currents of air are called winds^ and nearly 
all winds are caused, directly or indirectly, by convection. 

Winds are of great value ; they tend to keep uniform 
the temperature of the air, just as convection currents 
tend to keep uniform the temperature of heating water ; 
they bring pure air to large cities, carrying away the 
impure air ; they force pure air into poorly ventilated 
buildings ; they run windmills, drive ships, and serve 
many other useful purposes. 



146 ' HEAT [§§247-248 

247. Ocean Currents. — Just as it is with the atmosphere, 
so it is with the oceans. The heat of the sun causes the 
colder northern and southern waters to flow toward the 
equator, pushing upward the warm water, causing it to 
flow back toward the poles ; giving, in general, an under- 
current toward the equator and an upper current toward 
the poles. But the variations in the effect of the sun on 
the water, and the interference of the land, cause many 
irregularities in the currents. 

Convection currents in the ocean and other large bodies 
of water assist in preventing them from freezing in cold 
weather. The heat in the interior of the earth warms the 
sea bottom, and this in turn warms the water in contact 
with it, setting up currents which tend to keep the water 
above the freezing-point. At the same time, if the water 
on the surface cools, it contracts and sinks, until the entire 
body cools to four degrees, so that usually an enormous 
amount of heat is given out by the water before the freez- 
ing-point is reached. On the other hand, when the surface 
water does freeze, being lighter than that below, it remains 
on top, and, before the water below can freeze, all its heat 
must pass out, by the slow process of conduction, through 
the ice. So that such bodies of water, in temperate zones, 
seldom freeze at all, and when the}^ do it is only slightly ; 
while, if it were not for these factors, all such bodies would 
begin freezing at the bottom, and would in time probably 
freeze solid. 

248. Application of Convection. — Chimneys. A stove is 
so arranged that when a fire is started the air in the chim- 
ney is heated, and a convection current is started up the 
chimney because fresh air is being constantly forced in at 
the draft opening. In Fig. 68, the air is forced in at a by 
the pressure of the atmosphere. If a is closed, some air 
will still, usually, be forced through the cracks into the fire; 



§§ 248-249] 



TRANSFERENCE OF HEAT 



IV 




but if tlie clamper b is opened, the air will pass through 5, 
over the fire, and up the chimney, practically none going 
through the fire. The fire may be still 
further regulated by the damper c. 
The longer the chimney the stronger 
the draft, and, if e is opened, air passes 
in from outside, and the length of the 
chimney affecting the stove is only 
from the fire to c. When b is opened, 
there is practically no effective chim- 
ney, and the fire burns still less. 

In order to keep up a good draft of 
air, it is necessary not only to have a 
long chimney, but also to keep the 
air in the chimney warm. To avoid 
these expenses, it has been found 
best, in some cases, to force the air 
through the fire by some suitable apparatus, such as a fan 
run by an engine. In such cases there is, of course, little 

or no convection 

ir M I I I I 1 I I I I iFiriTf i current involved. 

The value of 
lamp chimneys is 
in causing con- 
vection currents, 
which constantly 
supply fresh air to 
the flame. 

249. Hot-air 
Heaters. — Build- 
ings are frequently 
heated by convec- 
tion currents of hot 
air. The principle of a hot-air heater for this purpose is 




£3 



£3 



148 



HEAT 



[§§ 249-251 



shown in Fig. 69. The air at a is heated by the furnace 
b ; cold air enters at cc and forces the hot air upward, as 
indicated by the arrows ; the hot air passes into the room 
to be heated, and there cools, and passes down again into 
the heater. Sometimes the cool air is allowed to pass 
outdoors, while fresh air passes into the heater from out- 
side. In this case no other ventilation is required, but in 
the former case much care should be used in ventilating. 

250. Hot-water Heaters. —Build- 
ings are also heated by convection 
currents of hot water, as indicated 
by Fig. 70. The water is heated in 
the heater at a ; becoming lighter, 
it is forced up by the cold water as 
indicated by the arrows, and passes 
through the radiator in the room 
to be heated. Radiators similarly 
connected with the heater may be 
placed in any room in the house, 
and so effective are the currents 
set up that the radiators may be 
but little higher than the heater, and yet be horizontally 
hundreds of feet away. 

251. Radiation. — A third manner by which the kinetic 
energy of heat is transferred from one body to another is 
called radiation. The heat from a hot stove may easily be 
felt when several feet away. In such cases it is evident 
the heat is not transferred by conduction, because when a 
metal screen is placed before the stove the heat is no longer 
felt, although the metal is a far better conductor than air. 
Nor can it be by convection, as the effect passes downward 
as well as upward. The heat, or its effect, acts radially, 
being radiated out in all directions ; and hence this man- 
ner of transferring the energy is called radiation. It is 




IS?t^^ 



Fig. 70. 



§§ 251-253] TRANSFERENCE OF HEAT 149 

by radiation that tlie heat of the sun affects us. All 
bodies are constantly radiating heat energy ; but as they 
also receive heat energy from surrounding bodies, their 
temperature is not necessarily lowered. 

252. Radiant Energy. — In such case, however, the 
heat itself — that is, the motion of the molecules — is not 
transferred. It is only the effect of this motion that is 
transferred. But, as it results in heating surrounding 
bodies, it is evident that energy in some way is transferred 
— energy is radiated out by the stove ; and this is spoken 
of as radiant energy. 

253. Ether. — Numerous investigations show that radi- 
ant energy is not transmitted by the molecules of the air or 
of any other substance. The energy passes through a vac- 
uum as readily as through air. The heat effect of incan- 
descent electric lamps is very noticeable, though the heated 
filament is in a vacuum. But it is inconceivable that 
energy can be transferred from one place to another unless 
it is transmitted by or through some medium. The 
enormous amount of energy which is radiated to us from 
the sun must have some medium for its transmission. 
Being impressed by this, and by other facts which indicate 
the same necessity, scientists have assumed that all space, 
not occupied by the atoms of matter, is filled with some 
medium which is capable of transmitting energy from one 
atom or system of atoms to another. It is supposed that 
the moving atoms set up disturbances in the ether ; that 
these disturbances, wdiich are forms of energy, travel out- 
wardly in all directions, and increase the motion of other 
atoms coming under their influence. In this waj^ it is sup- 
posed that the heat of one body, in the form of energy, is 
radiated through space to other bodies, as far as from the 
stove to the hand, or from the sun or even from the stars 
to the earth. 



150 HEAT [§§254-255 

EXERCISES 

1. Why do stove utensils frequently have wooden han- 
dles? 

2. Why will the small boy's tongue freeze to the iron pump- 
handle in very cold weather, when it will not freeze to the 
wooden handle ? 

3. What causes the hand to burn more readily in hot water 
than in air at the same temperature ? 

4. Explain, in a general way, how buildings might be cooled 
in summer by reversing the hot-air heater. 

5. At what temperature must water be to cause convec- 
tion currents by heating it on top ? by cooling it at the 
bottom ? 

6. Why is there seldom frost in mild weather near trees or 
buildings, or on cloudy nights ? 



SECTION 4. HEAT MEASUREMENTS 

254. Calorimetry. — Calorimetry is the process of meas- 
uring quantities of heat. We may wish to determine the 
quantity of heat required to raise the temperature of a 
substance, or to change its condition from a solid to a 
liquid, or from a liquid to a gas, or we may desire to find 
the total quantity of heat the body contains. And calorime- 
try is the process by which any of these quantities is 
determined. 

255. Heat Units. — In order to measure quantities of 
heat, as with any other measurement, we must have some 
standard quantity to refer to — we must have a unit 
quantity of heat. The most logical unit of heat is the 
amount required to raise the temperature of unit mass 
of some substance one degree. This is the unit chosen, 
and water is taken as the substance. Thus, the unit of heat, 
is the amount required to raise the temperature of unit 



§§255-258] HEAT MEASUBEMENTS 151 

mass of water one degree. We may take one pound of 
water heated through one degree Fahrenheit; one kilo- 
gram heated through one degree Centigrade. Or any 
other unit mass of water may be taken, bearing in mind 
always that the amount of heat involved in the unit is 
proportional to the amount of mass and to the increase in 
temperature. 

256. Calorie. — But, for reasons already given, the unit 
generally used in physics is the amount of heat required 
to raise one gram of pure water one degree Centigrade. 
This unit is called the calorie. 

257. Specific Heat. — If we heat in a beaker 200 g. of 
water, for a minute or two, and then heat an equal mass of 
mercury similarly, the temperature of the mercury will 
increase about 30 times as much as that of the water. Or, 
taking one gram of mercury, and making measurements, 
it will be found that the heat required to raise its tem- 
perature one degree Centigrade is .033 calories. So it 
takes .033 times as much heat to raise mercury one degree 
as to raise an equal amount of water one degree ; and this 
number is called the specific heat of mercury. Just as we 
call the specific gravity of a substance the ratio between 
its weight and the weight of an equal volume of water, so 
we call the specific heat of a substance the ratio between 
the respective amounts of heat required to raise its tem- 
perature and the temperature of an equal weight of water 
one degree. And as it takes one calorie to raise a gram 
of water one degree, evidently the heat required to raise any 
substance one degree ivill he its specific heat. 

The specific heat of all common substances except water 
is less than one. 

258. Heat required to raise Temperature. — In order, 
then, to find the heat required to raise the temperature of 
any substance, we have only to multiply the specific heat 



152 HEAT [§§ 258-259 

of the substance by its mass, and then by the degrees the 
temperature is raised. This is true, however, only in a 
general way, because the specific heat of most substances 
changes more or less as the temperature changes. For 
instance, while the specific heat of mercury is .033 at 0°, 
it is .032 at 200°. And the rule would not be true in any 
case where the physical condition of the substance was 
changed during the rise in temperature, as we shall now 
see. 

259. Heat of Fusion. — If we warm a vessel full of snow 
or ice, we shall find that its temperature will rise until 0° 
is reached, but that it will remain at 0° until it is all 
melted, although heat is being applied constantly. This 
indicates that heat is used in merely fusing the ice without 
raising its temperature. And the heat thus used in melt- 
ing one gram of ice is called the heat of fusion of the ice. 
This is true of any solid : when it is melting, a certain 
amount of heat, varying with the substance, is used, 
although the temperature remains constant ; and the 
amount required to melt one gram of the substance is 
called its heat of fusion. 

The heat of fusion is the energy required to overcome 
the cohesion between the molecules. Just as it requires 
energy to lift a stone away from the earth, so it requires 
energy to separate, or disconnect, the molecules of a solid 
sufficiently to turn the substance into a liquid. 

Just as a liquid gives off heat when it cools, so it gives off 
heat when it solidifies, although its temperature does not 
fall until the substance is entirely solidified. And it gives 
off just as much heat as is required to melt it. 

The heat required to melt a solid, or that is given off 
when a liquid solidifies, is frequently called latent heat of 
fusion. This use of the word latent, however, is incon- 
sistent with our j)resent conception of heat. 



§§ 259-261] HEAT MEASUREMENTS 153 

260. Amount of Heat of Fusion. — As already suggested 
one of the tasks of calorimetry is to measure the amount 
of heat required to change the substance from a solid to a 
liquid. With ice the task is not very difficult. If we 
place a dry piece of ice at 0° in a vessel containing a 
known mass of water at a known temperature, and then, 
as soon as the ice is melted, weigh the water and take its 
temperature, the increased weight will equal the mass of 
the ice melted, and the decrease in temperature times the 
mass of the original water will give the number of calo- 
ries required to melt the ice and raise its temperature to 
the final temperature of the water. Then by subtracting 
the calories required to warm the ice water, and dividing 
by its mass, we get the heat of fusion of the ice. 

To be accurate, however, corrections should be made for 
heat radiated away from or to the vessel, and for the heat 
required to change the temperature of the vessel, as it will 
assume about the same temperature as tiie water. 

The heat of fusion of ice has been found to be about 80 
calories, and it is much greater for ice than for any other 
common substance. 

261. Heat of Vaporization. — If we heat water until it 
boils, its temperature will rise no higher, no matter how 
vigorously it may boil, until the water is entirely vapor- 
ized. Yet every one is familiar with the fact that water 
boils into vapor rather slowly ; it is capable of receiving 
much heat after the boiling begins. This is due to the 
fact that much energy is required to overcome the cohe- 
sion of the water molecules for each other sufficiently to 
cause them to form a gas, and also to the fact that the air 
pressure has to be overcome sufficiently to give the steam 
far more room than is required for the water. The heat 
energy thus expended in vaporizing one gram is called the 
heat of vaporization of the water. 



154, HEAT [§§201-263 

It is the same with any liquid ; when it is vaporizing, 
although its temperature remains constant, mucli heat 
may be added. And the amount required to vaporize 
one gram of the substance after it lias reached the boiling 
temperature is called the heat of vaporization of the 
substance. This is called also latent heat. 

When any gas condenses into a liquid, just as much heat 
is given out as is required to vaporize an equal weight of 
the substance. 

262. Amount of Heat of Vaporization. — The heat of 
vaporization of water may be found by passing steam into 
a vessel containing a known mass of water at a known 
temperature. The increased weight will equal the mass of 
the steam condensed, and the increased temperature times 
the original mass will be the calories given off by the 
steam in condensing, and in cooling down to the final tem- 
perature of the Avater. To get accurate results the change 
of temperature of the containing vessel — the calorimeter 
— must be considered; the product of its specific heat, 
its mass, and its change in temperature Avill give the num- 
ber of calories imparted to it. 

If the water is at 100°, its heat of vaporization is about 
536 calories ; but if it is below 100°, the total heat re- 
quired to vaporize one gram will be 536 calories plus the 
amount required to raise its temperature to 100°, or one 
calorie for each degree. 

The heat of vaporization of water is much greater than 
for any other common substance. 

263. Natural Effects of Heat Capacity. — We find then 
that the specific heat, the heat of fusion, and the heat of 
vaporization are much greater for water than for any other 
common substance. This superior heat capacity has many 
important bearings in nature. It tends to keep the tem- 
perature of the air uniform. For instance, when it is 



§263] HEAT MEASUREMENTS 155 

snowing, the temperature rarely sinks very much below 
the freezing-point, because so much heat is given out 
by the moisture when the snow-flakes are formed ; and 
when the ground is covered with snow, the temperature 
rarely rises much above the freezing-point, because so 
much heat is used in melting the snow. 

Similarly, exposed bodies of water, while freezing, give 
off so much heat that the surrounding air is warmer than 
it otherwise would be. For this reason pails full of water 
are often placed in rooms to keep out frost. And, on the 
other hand, when the ice from these bodies of water thaws, 
the surrounding air is kept cooler. 

Also the temperature of air near large bodies of water 
is more uniform during all seasons of the year, because, 
when the temperature rises or falls, the great specific heat 
of the water allows it to absorb or give off, as the case may 
be, much heat, which tends to limit the rise or fall in tem- 
perature of the air. And, similarl}^ because of the large 
amount of heat absorbed or given off as water vaporizes or 
condenses, a rise or fall in temperature is limited by the 
increased vaporization or condensation that inevitably fol- 
lows. And this effect is greatly augmented by the vapor- 
ization or condensation taking place in the air itself, 
clouds, fogs, or mists being dissipated or formed with 
almost every change in temperature. 

Also the moisture in the air, by virtue of its great spe- 
cific heat, absorbs heat when the temperature tends to rise 
during the warm part of the day, and gives it off again 
during the cool part, thus tending to equalize the tempera- 
ture throughout the entire day and night. It is particu- 
larl}^ effective in this way in intercepting the rays from 
the sun to the earth during the day, and from tlie earth 
into space during the night. England's great physicist, 
Tyndall, has said : " The removal, for a single summer 



156 HEAT [§§263-265 

night, of the aqueous vapor from the atmosphere which 
covers England would be attended by the destruction of 
every plant which a freezing temperature could kill." 

264. Artificial Applications of Heat Capacity. — Hot- 
water heaters, such as are described in Art. 250, would be 
much less effective if it were not for the great specific 
heat of water, as far less heat would be carried with the 
same amount of circulation ; and, except where the radia- 
tors were nearly over the heater, the convection currents 
formed would be too slow to carry sufficient heat. And 
the basis of steam heating is the great heat of vaporization 
of the steam. The same amount of heat that is required 
to vaporize the water is given out to the surrounding sub- 
stances when the steam condenses ; hence the steam 
passing into the radiators on condensing gives out suffi- 
cient heat to keep the radiators and the surrounding air 
at the temperature desired. The value of hot-water bags 
for warming the feet is due to the great specific heat 
of the water. 

265. Total Amount of Heat. — Suppose now we wish to 
find the total amount of heat required to raise the tempera- 
ture of a body and to change its state. We have only to 
find the sum of the amounts required for each change. If 
we wish to raise the temperature of 12 g. of ice at — 10° to 
steam at 110°, we first consider the heat required to bring 
it to the melting-point. The specific heat of ice is about 
.5, hence to raise the 12 g. to 0° would take 12 x .5 x 10 
calories. To melt the ice would take 12 x 80 calories ; 
to heat to 100°, 12 x 100 ; to vaporize the water, 12 x 536 ; 
and as the specific heat of steam from 100° to 110° is .37, 
to heat the steam would take 12 x .37 x 10 calories. 

In working all such problems the student should first 
state the problem to himself in a general way, without 
reference to the values involved. For instance, here the 



§§265-267] HEAT MEASUREMENTS 157 

problem is to find tlie heat to warm the ice, then to melt 
the ice, then to heat the water, then to vaporize the water, 
and then to heat the steam. Then he should take each 
step at a time, as a single problem entirely independent of 
the other steps, and find its effect ; then consider the rela- 
tion between the several effects and combine them prop- 
erly. And in no case should a step be taken without 
seeing the reason ; there should be no guesswork. 

If the problem is at all complicated, it should be fully 
tabulated, somewhat as follows : — 

Heat to warm ice 12 x .5 x 10 = 60 calories, 

to melt ice 12 x 80 = 960 

to warm water 12 x 100 = 1200 

to vaporize water 12 x 536 = 6432 

to heat steam 12 x .37 x 10 = 44.4 



Total heat required 8696.4 calories. 

If the problem is to find the heat given off as a body 
cools, it is necessary only to keep in mind that exactly the 
same amount is given off as is required to heat the body 
through the same range of temperature. 

266. Absolute Zero. — If the heat of any body is due to 
the motion of its molecules, it is evident that if the motion 
were to cease, the body would have no heat — its tempera- 
ture would be absolutely nothing. This temperature is 
called absolute zero^ and it has been estimated in various 
ways to be about — 273° C. That is, it is supposed at 
about — 273° the motion of the molecules of all matter 
would cease, there would be no heat whatever, and the 
temperature would be absolutely zero. 

267. Absolute Temperature. — This makes it convenient 
to consider a temperature scale, beginning with absolute 
zero, and ranging upward indefinitely : thus — 272° C. 



158 UEAT [§§267-269 

would be 1° absolute temperature ; — 173° C. would be 
100° absolute, and so on. Absolute temperature then would 
be 273° more than Centigrade. Such a scale has been 
adopted, and to pass from Centigrade to absolute tempera- 
ture we have only to add 273° to the Centigrade reading. 

268. Absolute Amount of Heat. — Although we can esti- 
mate quite closely what the absolute temperature of a body 
is, and how much its temperature must be lowered to 
remove all the heat it contains, still it is impossible to 
estimate at all closely the absolute amount of heat the body 
contains, or the amount it would give off if cooled to zero 
absolute; because the specific heats of all substances change 
with the temperature, and we have no way of knowing 
what the specific heats of substances are at very low 
temperatures. 

269. Coefficient of Expansion. — We have now to discuss 
measurements of the effects of heat ; and the only effect, 
aside from change of physical condition, that we are inter- 
ested in is increase of size by increase of heat. As we 
have already seen, when a metal bar is heated, it increases 
in length ; and the amount of increase of a unit length of 
the bar when heated from 0° to 1° is called its coefficient 
of expansion. Hence, in order to find what the increase 
of any bar will be when heated, we have only to find the 
product of its length, its increase in temperature, and its 
coefficient of expansion. Thus the coefficient for iron is 
.000012 ; and we have, increase = .000012 It, Avhere I is the 
length and t the increase in temperature. 

The number expressing the coefficient is simply the ratio 
between the total increase per degree and the total lengtli ; 
so it is immaterial in what units the lengtli is expressed. 

The reason for calling .000012 the coefficient is evident 
from the above equation ; it is the coefficient of It, accord- 
ing to algebra. 



§§270-272] HEAT MEASUREMENTS 159 

270. Linear and Cubical Coefficient. — The linear coeffi- 
cient of expansion is tlie increase in lengthy while cubical 
coefficient is the increase in volume. The cubical coefficient 
for the same body is a little more than three times the 
linear, as the expansion is considered in three directions 
instead of one. 

For instance, consider a cube of iron with edges 1 cm. If 
heated through 1°, each dimension would become 1.000012 
cm. Its volume then would be (1.000012)3 q^z q^ 1.000036 
+ cm. 3, and the cubical increase would be .000036 cm.^ 
per unit of volume for 1°. 

The linear coefficient is usually considered in case of 
solids, and the cubical coefficient in case of liquids and 
and gases. 

271. Expansion of Solids. — If a bar of iron and one of 
copper, of equal lengths, are heated equally, the copper bar 
will become longer than the iron ; hence the coefficient of 
expansion is greater for copper than for iron. In fact, as is 
indicated by the table, p. 372, the coefficient varies with 
most substances. So, in order to find the increase in length 
which any required increase in temperature will cause, we 
must know the coefficient of the particular substance 
under consideration. 

272. Expansion of Gases. — On the other hand, it has 
been found that the coefficient of expansion is practically 
the same for all gases. So, if we have the coefficient for 
any gas, we need know only the original volume and the 
increase in temperature of any other gas in order to find 
its increase in volume when heated. Now, the coefficient 
of expansion of any gas is approximately the reciprocal of 
its absolute temperature. Thus, 0° C. is 273° absolute; 
and if a cubic centimeter of gas at that temperature is 
heated one degree, its increase in volume will be 2Y3 cm. 3. 
And, similarly, if heated one degree when the gas is at 



160 HEAT [§§272-273 

20° C, or 293° absolute, the increase will be gig cm.s. 
Hence, to find ajDproximately the increase in volume of 
any gas when heated, we have only to find the product of 
its original volume, its rise in temperature, and the recip- 
rocal of its absolute temperature. 

273. Law of Charles. — Taking a gas then at, say, 273° 
absolute temperature, if it is heated through 273° more, its 
volume will be doubled — if its temperature is doubled, 
its volume will be doubled. And we shall find, with any 
gas, the increase in volume is approximately proportional to 
the i7icrease in absolute temperature^ if the pressure is con- 
stant. This is known as the law of Charles, as it was 
first deduced by a French physicist named Charles. 



EXERCISES 

1. Taking as a unit of mass 1 lb., how many units of heat 
are required to raise the temperature of 12 lb. of water from 
60° to 100° ? 

2. How many calories would be required ? 

3. What is the value of a unit of heat based on the pound 
in terms of units based on the gram ? — that is, what is the value 
of the pound heat-unit in terms of the gram heat-unit ? 

4. What is the value of the kilogram heat-unit in terms of 
calories ? in terms of the pound heat-unit ? 

5. How many calories are required to heat 20 g. of water 
through 40° C. ? through 45° F. ? 

6. How many calories to heat 25 g. of water from 32° to 
180° F. ? 

7. How many calories to melt 15 g. of ice and raise the 
temperature of the water formed to 100° ? 

For the specific heats, if required, refer to table, p. 372. 

a How many calories to heat 200 g. of ice, and the result- 
ing water and steam, from — 12° to 110° ? How many to heat 
12 lb. of mercury from 0° to 125° ? 



HEAT MEASUREMENTS 161 

9. How many pound heat-units to melt 10 lb. of ice ? How 
many to vaporize 10 lb. of water at 100° ? 

10. If 11 g. of ice at - 8° is placed in 100° g. of water at 80°, 
what will be the resulting temperature ? 

11. If 20 g. of steam at 108° is condensed in 385° g. of water 
at 0°, what will be the resulting temperature ? 

12. How many grams of water could be heated from 0° to 25° 
by the heat given off by 300 g. of mercury when cooled from 
100° to 0° ? 

13. What would be the specific heat of a substance, if 12 g. 
cooled through 8° would heat 2 g. of water 4° ? 

14. AYhat would be the increase in length of a bar of iron 
heated through 8°, if its original length was 100 cm. ? if its 
original length was 100 in. ? 

15. How much would the rails of a railway 100 mi. long 
increase in length if the temperature rose from — 12° to 48°, 
the coefficient of expansion for that range of temperature 
being .00001322 ? 

16. What is the coefficient of expansion of a bar that expands 
.003 ft. when heated from 0° to 28°, if its original length Avas 
5 ft. ? if its original length was 160 cm. ? 

17. What is the length of a bar of iron which expands 1 mm. 
when heated 400° ? 

18. What would be the change in circumference of a wagon 
tire 4 ft. in diameter if heated from 0° to 700° ? If placed on 
the wheel at that temperature, how much would it shrink in 
diameter on cooling to 12° ? 

19. Find the volume, at 12°, of a gas whose volume is 20 cm.^ 
at 0°, if the pressure remains constant. 

20. Find the increase in volume of 15 cm.^ of oxygen when 
heated from 18° to 100°. 

21. A gas increases in volume 3 cm.^ when heated through 
70°. If its original volume was 12 cm.^, what was its original 
temperature ? 

22. How much will 48 cm,^ of air decrease in volume when 
cooled from 100° to 10° ? 



162 HEAT [§§ 274-276 

23. What will be its volume if cooled to — 10° ? 

24. The original Brooklyn bridge is 5989 ft. long, approaches 
and all. If composed of continuous bars of iron, what would 
be its increase in length when the temperature changes in the 
course of the year from — 25° to 33° ? 



SECTION 5. HEAT AND WORK 

274. Production of Heat by Work. — About the end of 
the eighteenth century Count Rumford, at Munich, sur- 
prised the world by causing water to boil with the heat 
generated while boring a cannon with a dull drill. Since 
then many experiments have shown that heat is always 
generated when work is performed. Although by far the 
greater portion of the work may produce no heat, yet the 
friction which results will always generate some heat; and 
any percussion or agitation accompanying the work will 
also cause heat. 

275. Heat Equivalent of Work. — Count Rumford, by his 
experiments, found that friction, as a source of heat, was 
inexhaustible ; and he inferred that the heat so generated 
was proportional to the amount of work spent in over- 
coming the friction. He also inferred, what has since 
been proven, that, wdien work is spent in any way in pro- 
ducing heat, the amount of heat produced is exactly 
proportional to the work performed — in other words, that 
wor\ has a. definite heat equivalent. 

276. Measurement of Heat Equivalent. — It was not, 
however, until the middle of tlie nineteenth century that 
Count Rumford's conclusions were accepted as true. At 
that time Joule, of England, by a series of experiments 
extending over many years, not only showed that work 
has a definite heat equivalent, but also determined very 
accurately the value of that equivalent. That is, he 



§§270-278] HEAT AND WORK 163 

determined the number of heat-units that are equivalent 
to one work-unit. 

We have already seen that shaking or agitating water 
in any way will increase its temperature ; the work of 
agitation is turned into heat. If, then, we note the in- 
crease of temperature when water is agitated, and multiply 
this increase by the mass of the water, we shall find the 
amount of heat which the work produces. And if we 
measure the amount of work used, we can readily deter- 
mine the heat equivalent of the work. In some of Joule's 
experiments he agitated water in a vessel by means of 
paddles driven by a falling mass. He determined the 
units of work performed by the mass and the units of 
heat produced in the water, and thus derived the heat 
equivalent. Other methods have since been pursued by 
numerous investigators, and the heat equivalent has been 
very accurately determined. 

277. Heat Equivalent of the Kilogr ammeter. — Probably 
the most accurate measurement of the heat equivalent was 
made in 1879, by Professor Rowland, at the Johns Hopkins 
University. He found that approximately .427 kilogram- 
meters of work were required to produce one calorie of 
heat ; and consequently the heat equivalent of one kilo- 
grammeter would be the reciprocal of this number, or 
2.34 calories. 

278. Performance of Work by Heat. — When the piston 
of the fire syringe mentioned in Art. 198 is pressed down- 
ward, heat is produced by the work. When the pressure 
of the hand on the piston is removed, the heat energy in 
the confined air is sufficient to push the piston back to its 
original position, and tvork is thus 2^erfo7'med hy the heat. 
There are numerous ways in which heat may be made to 
perform work ; some of them, of great practical importance, 
we will consider. 



164 HEAT [§§ 279-280 

279. Heat-engines. — Any machine which can be made 
to perform work by applying heat to any of its parts, may 
be called a heat-engine. Suppose a bar of iron is so 
arranged that, when it expands and contracts on being 
heated and cooled, it will work a lever back and forth; 
such an apparatus would be a machine capable of per- 
forming work, and might be called a heat-engine. Many 
heat-engines have been constructed, but the only ones 
which have proven of much practical value are the gas- 
engines and the steam-engines. 

280. Gas-engines. — If some combustible gas, such as gas- 
oline vapor, or coal gas, is mixed with air and passed into 
the end of a cylinder, such as is indicated in Fig. 71, through 
the opening ^, and is then ignited, the heat generated will 
cause the gas produced by the combustion to expand ; and 
if there is a piston in the cylinder, arranged as indicated, 

so as to separate" the 

gas from the other 

V-^_fyv,:P/"X>"^-4\ end of the cylinder, 

i '^'- ''r I ^^^ expanding gas 

will drive the piston 
toward the other 
end ; and thus, by means of the connecting-rods and the 
crank, the wheel will be made to rotate. If the wheel 
is sufficiently massive, when once started it will continue 
to rotate because of its inertia, and will drive the piston 
back again to the original position. The piston will 
thus drive the burned gas out of the cylinder through the 
port p, which in the meantime has been opened by the 
rod r; and when the piston goes back the second time, it 
will again be driven forward by the explosion of a fresh 
supply of gas. The rod r also closes the opening g at the 
proper time. 

This is a very general description of the ordinary gas- 




p 

w 

Fig. 71. 



§§280-281] 



HEAT AND WORK 



165 



engine, a common form of which is sliown in full in Fig. 
72. Gas-engines are made in various styles and for dif- 
ferent combustible gases and liquids. They are very 
efficient and convenient, but are limited in power. 




Fig. 72. 



281. steam-engines. — The most useful machine for 
performing work by means of heat is the steam-engine, 
with which nearly every one is more or less familiar. The 
principle involved in the steam-engine is somewhat similar 




to that of the gas-engine, the main difference being in the 
use of the expansive power of steam to actuate the piston 
instead of the explosive force of a burning gas. 

Water is heated in the boiler B (Fig. 73). The steam 
which is produced is confined in the boiler until the press- 



1G6 



HEAT 



[§281 




i'>( 






Fig. 74. 



ure becomes high, frequently as high as ten times the 
pressure of the atmosphere. The steam under this high 
pressure is passed through the pipe P into the steam-chest /S', 

and then through the port 
p into the end of the cylin- 
der C. The high pressure 
of the steam enables it to 
push the piston toward the 
other end of the cylinder, 
and thus cause the fly- 
wheel to rotate. As the 
wheel rotates it actuates, 
by means of suitable con- 
necting-rods, the sliding 
valve FJ and thus closes the 
port^. The steam in the end of the cylinder is thus shut 
off from the boiler ; but as it has enormous elastic force, 
it expands, and pushes the piston on farther, to the other 
end of the cylinder. The steam then enters at the port p'^ 
and, in the same manner, 
pushes the piston back. 
The piston in turn pushes 
the dead steam which is 
in the other end of the 
cylinder out through the 
port^, which in the mean- 
time has been opened by the 
connecting-rod r ; and from 
the steam-chest the dead 
steam passes out through 
the exhaust port e. The 
process is then repeated continuously so long as steam 
is allowed to enter the steam-chest. 

Figures 74 and 75 show the cylinder and steam-chest 




§§281-283] HEAT AND WORK 167 

enlarged, so that the process may be more easily followed ; 
74 shows the steam just beginning to force the piston 
back ; and 75 shows the piston travelling in -the opposite 
direction just as the steam from the steam -chest and 
boiler is shut off from the cylinder. 

282. Mechanical Efficiency of Heat. — It is evident that, 
in case of the heat-engine, the heat is not all effective in 
performing work. With the gas-engine heat is imparted 
to the cylinder and the piston by the hot gas, and this 
heat is of course in no way effective in running the 
engine. Instead, it is merely transferred by conduction or 
by convection to surrounding substances, and is then 
replaced by more heat from the gas. Also the friction of 
the moving portions of the engine has to be overcome. 
So that the energy represented by the useful work per- 
formed may be far less than the energy of the heat applied 
to the engine. With the steam-engine even more heat is 
wasted ; heat is radiated from the boiler and from the pipes 
conveying the steam to the engine ; and a large amount 
of heat from the burning coal passes up the smoke-stack 
with the smoke. With the best-constructed steam-engines 
the amount of heat that is effectiv^e in performing useful 
work is less than 15 per cent, of the heat generated by the 
burning coal. 

The ratio between the energy of the heat that is effec- 
tive in performing useful work and the total energy of 
the heat is called the mechanical efficiency of the heat. 

283. The Mechanical Equivalent of Heat. — Although 
much heat is wasted in running heat-engines, yet the heat 
which is thus wasted has power of performing work just 
as has the heat which is effective. So it is evident that in 
every given amount of heat there must be a corresponding 
amount of energy ; and a corresponding amount of work 
could be performed if we were able to make all the energy 



168 HEAT [§§283-287 

effective. In other words, a calorie must contain always 
a definite amount of energy. And as energy is measured 
by the amount of work it can perform, a calorie must 
be equivalent to a definite number of work-units, just as 
a kilogrammeter is equivalent to a definite number of 
heat-units. The amount of work to which the heat-unit 
is equivalent is called the mechanical equivalent of heat. 

As implied in Art. 277, the equivalent of one calorie is 
.427 kilogrammeters ; it is approximately 42,000,000 ergs. 

284. First Law of Thermodynamics. — All that we have 
been discussing here is embodied in what is called the 
first law of thermodynamics. Thermodynamics refers to 
the mechanical relations of heat, and the law states that 
definite amoimts of heat are always equivalent to propor- 
tional amounts of ivork. 

285. Refrigeration. — Let us now consider the relation 
between heat and work when bodies are cooled instead of 
heated. The process of cooling bodies is called refrigera- 
tion. It will be well to consider briefly the theory involved 
in refrigeration, the effects on substances, and practical 
applications of refrigeration, each of which involves the 
relation of heat to work. 

286. Methods of Cooling. — We have seen that substances 
may be heated by conduction, by absorption, by convec- 
tion, or hy having ivork performed upon them. Likewise 
substances may be cooled by conduction, by radiation, by 
convection, or hy performing ivorh upon other substances. 

287. Cooling by Conduction. — A body will cool by con- 
duction whenever it is in contact with other bodies cooler 
than itself, because its heat energy passes into the cooler 
bodies. And it will continue to cool until it reaches the 
same temperature as that of the surrounding bodies. But 
having reached that temperature, evidently it will cease 
cooling. 



§§287-290] HEAT AXD WORK 169 

This method of coolmg is adopted whenever objects are 
placed on ice. Not only is the ice ordinarily cooler than 
the objects, but it requires so much heat to melt the ice 
and to warm the resulting water, that it is very effective 
in cooling. 

288. Cooling by Radiation. — As indicated in Art. 251, 
all bodies continually lose their heat by the radiation of 
their energy into the surrounding space. At the same 
time, they are constantly absorbing energy from surround- 
ing space, which has been radiated by other bodies. Hence 
bodies will cool in this way only so long as they receive 
less heat energ}^ than they lose. And this will be the case 
only so long as they are warmer than surrounding bodies. 

289. Cooling by Convection. — Ordinarily, when the upper 
surface of a fluid is cooler than the main body of the fluid, 
convection currents are set up by the sinking of the cooler 
fluid because of its greater density. Hence, a fluid may 
be so cooled as long as heat is being removed from its 
upper surface by conduction or radiation. 

\Yhen ice is placed in refrigerators, cooling is carried on 
usually by each of these methods, — conduction in case of 
bodies actually in contact with the ice ; radiation by bodies 
not in contact, as the ice absorbs more heat energy than it 
radiates ; and convection by all bodies in the refrigerator 
except the ice, because convection currents are constantly 
caused by the ice cooling certain portions of the air more 
than other lower portions. 

As convection depends upon conduction or radiation to 
cool the higher portions of the fluid, it is evident that the 
cooling can continue only so long as the fluid is warmer 
than surrounding bodies. 

290. Second Law of Thermodynamics. — The fact that 
bodies cannot be cooled by any of these methods below the 
temperature of surrounding bodies is implied by the second 



170 HEAT [§§290-291 

law of thermodynamics, which states : When a body becomes 
cooler than its surroundings, the heat lost is transformed into 
tvork. As no work is performed directly by the heat, in 
case of conduction, radiation, or convection, according to 
the law these methods are not sufficient to cool bodies 
below the temperature of surrounding bodies. 

291. Cooling Mixtures. — We come now to the last 
metliod of cooling, that in which a substance cools itself 
by performing work ; the heat energy is transformed into 
work. A very common way of doing this is by the use of 
cooling mixtures. It is well known that when ice and 
common salt are brought in contact, the temperature of the 
two falls below that of the ice. This may easily be tried 
by simply mixing a handful of salt and about three times 
as much snow or pounded ice at 0°. It will be found 
that the temperature of the mixture rapidly falls consider- 
ably below the melting-point of the ice. 

At the same time it will be noticed that the mixed solids 
rapidly become liquids ; at least the ice melts more rapidly 
than when not mixed, and the salt also becomes liquefied. 
Now, when any solid is fused, work is done upon it ; the 
molecules are usually driven farther apart ; at least the 
force of cohesion between them is weakened by increasing 
the relative distances between them or changing their rela- 
tive positions ; and in either case the potential energ}^ is 
increased. Just as work is j)erformed when a body is 
moved away from the earth, weakening the force of gravi- 
tation and increasing the potential energy of the body, 
so is work performed when molecules are moved farther 
apart. Hence, we find, while the ice and salt cool, the 
heat which they lose is transformed into the work of 
fusion. This being the case, the cooling goes on even 
when the temperature of the mixture is considerably below 
that of the surroundings. 



§§ 291-293] HEAT AND WORK 171 

This method of coolmg is used to an enormous extent in 
making ice-cream, ices, and for similar purposes. When 
about three parts of snow are thoroughly mixed with one 
part of salt, a temperature of — 21° can be obtained. 
Various other freezing mixtures are used, some of which 
are far more effective in reducing the temperature than 
snow and ice. When liquid sulphur dioxide is mixed with 
a proper amount of solid carbon dioxide, a temperature of 
— 82° may be obtained. 

292. Cooling by Expansion. — When the piston of the 
fire syringe (Fig. 65} is quickly pressed downward, the 
heat which is produced in the confined gas is sufficient to 
push the piston back to its original position against the 
atmospheric pressure. But, in doing this, the gas also 
cools down to its original temperature ; the heat gener- 
ated by the compression is transformed into the work 
required to raise the piston. When the hot gas in the 
cylinder of an engine expands, and pushes the piston for- 
ward, the gas becomes cooler ; the heat is transformed into 
the work required to push the piston forward. And in 
every case where a gas expands, and in doing so performs 
work, the gas cools. 

293. Theory of Cooling by Expansion. — When a gas is 
compressed its temperature is increased, probably because 
the motion of the molecules is increased. A boy strikes 
the bat toward the approaching ball in order to produce 
on the ball a greater effect than would result if the bat 
were held stationary. Similarly, the motion of the piston 
toward the molecules by which it is being bombarded pro- 
duces on the molecules a greater effect than would result 
if the piston were stationar}^ In either case the kinetic 
energy produced is greater than would be produced if the 
body were stationary. If the bat, or the piston, is station- 
ary, the ball, or the molecule, receives no increase of kinetic 



172 HEAT [§§293-294 

energy ; if the bat, or the piston, is moving forward, the 
kinetic energy of the ball, or the molecule, is increased — 
the molecule is heated. 

On the other hand, if the molecules push the piston hach^ 
their motion is decreased. The boy, on catching the ball, 
allows it gradually to come to rest by moving his hands 
backward in order to diminish the concussion ; more time 
is taken in overcoming the inertia ; more work is per- 
formed and less heat is generated. Just as less kinetic 
energy is imparted to the ball when the bat is held sta- 
tionary than when it is moving forward, so still less is 
imparted when the ball drives the bat backward — per- 
forms work upon it ; so the ball receives less energy than 
it imparts. Similarly, when the molecules are able to 
drive the piston backward, they have, after the impact, less 
kinetic energy than they would have if the piston were 
held stationary — less than they had before the impact. 

At the same time, if the bat was moved backward by 
the hand as the ball approached, and was then held station- 
ary as the ball struck, as much energy would be imparted 
to the ball as if the bat had not been moved. And, simi- 
larly, if the piston is moved backward by an external force 
sufhcient to overcome the pressure of the air, so that no 
work is performed upon it hy the confined gas, as much 
energy will be imparted to the molecules as if the piston 
had not been moved, as much energy as they impart to the 
piston, and the gas will not he cooled. 

Hence, a gas cools when it expands, but does so only 
because the heat is used in performing work ; and the 
work performed is proportional to the heat lost. 

294. Cold Storage. — This method of cooling has impor- 
tant applications. In order to preserve meats and vege- 
tables they are frequently placed in cold storage ; that is, 
stored in boxes or rooms, the air of which is kept about at 



§§ 294-295] HEAT AND WORK 173 

the freezing-point. Many methods, differing in detail, are 
employed to cool the air ; but in general the ordinary 
method is somewhat as follows : 

A tank full of ammonia water is warmed until the 
ammonia is driven off. as a gas. This gas is compressed, 
in some cases by its own pressure as it is changed from a 
liquid to a gas, in other cases by a compression pump. 
When compressed sufficiently it becomes a liquid. It is 
then allowed to cool, compression and liquefaction having 
raised its temperature. Then it is allowed to evaporate 
and expand, absorbing much heat from its surroundings. 
In order to more effectually absorb heat from the store- 
room, tlie expanding ammonia is frequently surrounded by 
brine, and this, on becoming ten or fifteen degrees below 
tlie freezing-point of water, is passed through the store- 
rooms in pipes. The ammonia absorbs the heat from the 
brine, and it in turn absorbs the heat from the air in the 
rooms. 

295. Artificial Ice. — The making of artificial ice is fast 
becoming a great industry. The principle involved is 
about the same as with cold storage. The cold brine is 
passed around vats full of water, and sufficient heat is thus 
abstracted from the water to cause it to freeze. 

It is interesting to note that frequently the whole pro- 
cess of refrigeration is the result of the application of heat. 
On heating the tanks of ammonia water the gas driven off 
is liquefied by its own pressure ; it loses its increased heat 
by conduction and radiation ; it expands and cools, and 
after cooling the brine, it is absorbed by the same liquid 
from which it was driven. And even if compression 
pumps or other machines are used, ordinarily they are 
actuated by heat engines. The process is effective because 
the compressed gas gives up its increased heat to surround- 
ing bodies^ and then cools still more on expanding. 



174 HEAT [§§296-297 

296. Liquefaction of Gases. — Another application of this 
method of cooling is to the liquefaction of gases, and par- 
ticularly of the air. Ammonia and some other gases, which 
have condensing temperatures not much below 0°, may be 
liquefied at the ordinary temperature by compression alone, 
because increased pressure raises the boiling-point. But 
many gases, especially those composing the air, cannot, at 
the ordinary temperature, be liquefied, no matter how 
much they are compressed. In order to be liquefied they 
must be not only compressed but also cooled. When so 
treated, any gas may be liquefied and even solidified. 

The air which is to be liquefied is confined in tanks, and 
is put through several successive steps of compressing and 
cooling. It is compressed first until its elastic force is, 
perhaps, 75 lb. per square inch ; it is then allowed to cool 
to the ordinary temperature by passing it through pipes 
surrounded by water. It is then compressed to several 
hundred pounds, and allowed to cool ; and then compressed 
to, perhaps, 2500 lb., and again allowed to cool. It thus 
loses an enormous amount of heat. Some of this highly 
compressed gas, or air previously liquefied, is then allowed 
to issue from a jet, and as it expands it surrounds the 
air to be liquefied, and cools it sufficiently to cause it to 
liquefy. The evaporation and expansion of a small amount 
of liquid air is thus able to cool a comparatively large 
amount of compressed air sufficiently to liquefy it. This 
is because so much heat is given up to its surroundings by 
the air being liquefied when it is compressed. 

297. Heat and Energy. — We thus see the intimate rela- 
tion which exists between heat and work ; heat may be 
generated by work, and it may be transformed back again 
into work. And this shows also a warrant for calling 
heat a form of energy. Energy is the power of perform- 
ing work, and heat has power of performing work. 



§§ 298-300] HEAT AND WORK 175 

298. Convertibility of Energy. — It is also evident that 
heat may be transformed or converted into other forms 
of energy. It may be converted into potential energy of 
masses by raising weights, or into kinetic energy of masses 
by forcing the cannon-ball from the cannon, or into 
potential energy of molecnles by fnsing or evaporating 
substances. And any of these forms of energy may be 
converted into kinetic energy of molecules, which is heat. 

This attribute of energy, which allows it to be converted 
from one form to another, is called the convertihility of 
energy. 

299. Conservation of Energy. — At the same time, when- 
ever there is an increase or decrease of energy of any of 
these forms, it is because there is a corresponding decrease 
or increase of energy of some other form. When a sub- 
stance is heated, other than by mere transference of heat, 
work is done upon the substance and a corresponding 
amount of energy of some form is used in performing the 
work. When potential energy appears in the form of a 
raised weight, an amount of energy exactly equal to that 
potential energy which appears, has been used. In other 
words, when energy is converted from one form into 
another, there is neither loss nor gain of energy, the total 
amount at the end being exactly equal to the total amount 
before the conversion. Energy, in fact, can in no way be 
either created or destroyed ; the total amount of energy 
never changes; it is always conserved. This is a great 
fundamental principle of all science, and is known as the 
conservation of energy. 

300. Perpetual Motion. — The conservation of energy is 
the great stumbling-block for those seeking to discover some 
form of perpetual motion — some machine which will run 
continuously without the assistance of any external force. 
So long as there is any friction whatever about the machine. 



176 HEAT [§§300-303 

energy must be used in overcoming the friction, and the 
total energy in the system will constantly decrease, unless 
there is external assistance. He who seeks to find per- 
petual motion should first seek to show that the law of 
the conservation of energy is untrue, as the discovery of 
such motion necessarily involves the untruth of the law. 
And, having found the law to be untrue, he need go no 
farther, because fame and fortune will then be his for the 
asking, as he will stand near the head of physicists. But, 
as no fact that is evidence of the untruth of the law has 
been discovered by the most searching investigations of 
the best scientists of the past fifty years, and as it is con- 
firmed by innumerable facts, it is not likely to be proven 
untrue. 

EXERCISES 

1. What is the heat equivalent of 1 gram-meter ? of 1 kilo- 
grammeter ? of 1 foot-pound ? 

2. How many gram-meters of work would be required to 
melt 100 g. of ice ? 28 lb. of ice ? 

3. How many gram-meters of work would be required to 
heat a kilogram of water at 0° sufficiently to cause it to boil ? 

4. With a good engine, out of every 100 units of heat applied 
about 30 units pass off through the chimney, and about 50 units 
are carried away with the exhaust steam. If the remainder 
is utilized in performing work, what is the efficiency of the 
engine ? 

5. If 6 units are used in overcoming friction and are other- 
wise wasted, what is the efficiency ? 

6. If the amount of heat generated by burning a kilogram 
of bituminous coal is 8000 kilogram heat-units, how much work 
could be performed with it, if the efficiency of the heat was .13 ? 

7. If 5184 gram-meters are required to generate 12 calories 
of heat, what is the mechanical equivalent of the heat ? 

8. How many ergs of work could be performed by 18 calories 
of heat, if 80 % of the energy was wasted ? 



CHAPTER VII 

ELECTRICITY 
SECTION 1. MAGNETISM 

301. Magnets. — Magnets are bodies of iron, steel, or 
some ore of iron, whicli have the power of attracting iron 
or steel, or, to a slight degree, nickel and cobalt. 

Magnets of iron or steel are called artificial magnets, 
and are magnetized by processes which w^e will discuss 
later. One of the iron ores, magnetite, or lodestone, how- 
ever, is magnetized when taken from the earth, and such 
a piece of ore is called a natural magnet. 

302. Magnetic Needles. — If a magnet is suspended so 
that it may swing freely, it is called a magnetic needle. 
If such a magnet is not near any other magnetic sub- 
stance, it will swing and come to rest pointing nearly 
north and south. The end which points toward the 
north we call the -H, or north-seeking j^ole, or simply the 
north pole; and the end which points toward the south 
we call the — , or south-seeking pole. 

303. The Mariner^s Compass. — The mariner's compass 
consists of a small magnetic needle, consisting of a rod 
of magnetized steel suspended so that it may swing freely 
over a circular scale which is so graduated as to show ac- 
curately the direction of the ship's course. The compass 
does not always point exactly north and south, and the 
variation, or declination, is not the same at all points upon 
the earth's surface. 

N 177 



178 ELECTRICITY [§§ 304-307 

304. Temporary and Permanent Magnets. — Procure a 
piece of soft iron — a wrought nail is good — and a piece of 
watchspring, which is steel. Stroke the iron from end to 
end, always in the same direction, upon one end of a per- 
manent magnet, and then test it for magnetism by thrust- 
ing it into a mass of iron filings. It will be found that it will 
pick up very few. Again stroke it, and, holding the end 
which last leaves the magnet in contact with the magnet, 
again test. Now remove the magnet and notice that 
nearly all of the iron filings are dropped. Repeat with 
the steel, and notice that when not in contact with the 
magnet, it retains a much greater amount of magnetism. 
Such a piece of steel, which retains its magnetism, is called 
a permanent magnet ; while the iron, which retains its 
magnetic power only while under the influence of some 
other source of magnetic attraction, is called a temporary 
magnet. 

305. Action of Magnetic Poles upon each other. — Sus- 
pend a magnet so that it can swing freely, and bring the 
north pole of another magnet near its north pole, and it 
will be found that they will repel each other ; but bring 
a south pole near a north pole and the two attract. Thus 
the law : Like poles repel, and unlike poles attract each 
other. 

306. Effect of Distance. — It will be found that the 
magnitude of the attractive or repellent force of a mag- 
netic pole depends upon the distance between it and the 
body acted upon. In case of two poles the attraction or 
the repulsion is directly proportional to the product of the 
strengths of the poles and inversely proportional to the 
square of the distance between them. 

307. Magnetic Induction. — Procure a soft iron nail and 
a strong permanent magnet. Hold the head of the nail 
near, but not touching, the north pole of the magnet, and 



§§ 307-309] MAGNETISM 179 

thrust the other end of the nail into a mass of iron filings. 
A quantity of the filings will be picked up by it, but, if 
the magnet be removed, nearly all will be dropped. This 
action of a magnet upon a piece of iron is called magnetic 
induction. 

A test will show that the nail has two poles, and that 
the pole farthest from the inducing north pole is also a 
north pole (Fig. 76). A piece of steel used in place of the 
nail will show much less mag- 
netism than the iron, but will ^ ^ ^ |n s] 
retain more of its magnetism yig. 76. 
after the removal of the induc- 
ing pole. Thus we are led to believe that substances 
which become magnetized readily lose their magnetism 
easily, while those which are magnetized with difficulty 
retain their magnetism longer. 

308. Effect of breaking a Magnet. — If a piece of watch- 
spring is magnetized, and then broken in the middle, it 

will be found that each piece 
is a perfect magnet, with two 
poles, arranged as in Fig. 77. 
If each piece is again broken, 
the smaller pieces will still be 
magnets, each with a north and 
a south pole, as indicated. This breaking may be carried 
on indefinitely ; and every piece, no matter how small, 
will be a complete magnet. 

309. Theory of Magnetism. — If a small glass tube is 
nearly filled with iron filings, or a long pile of filings is 
placed upon a sheet of thick paper, and one pole of a mag- 
net is drawn from end to end from below, as shown in 
Figs. 78 and 79, it will be seen that the bits of iron stand 
up as the pole passes, one end of each seeming to be at- 
tracted, and the other repelled ; and that, after the pole has 



N 






s 


1 1 


N 




S N 


s 


1 




< i 




N 
1 


-^r 


-^^ 


S N S 






Fig. 77. 





180 



ELECTRICITY 



[§309 



passed, the bits of iron, which have stood u^ on end, turn 
over and lie in rows which are more or less definite accord- 
ing to the strength of the magnet used and the number of 
times which it has been passed along. If, now, the pile of 




Fig. 78. 



Fig. 79. 



filings or the tube is tested with a compass, it will be found 
that one end repels and the other end attracts the north 
pole of the magnetic needle. Shake the tube or stir the 
pile of filings up, and it will be found that all signs of 
magnetization have disappeared. 

Tills experiment and the one with the broken magnet 
lead us to believe that the individual molecules of a piece 

of iron are little magnets, 
and that a piece of iron or 
steel is a magnet or not, 
according as the molecules 
are properly arranged. It 
would seem that, when the 
molecules are arranged so 
that a majority of their north 
poles point in one direction, 
and the south poles in the opposite (Fig. 80), the piece 
of metal becomes a magnet ; and a perfect magnet would 
be one in which all of the molecules are arranged with 
their like poles in exactly the same direction. 

This latter condition is one that is probably never 
attained. When the molecules are lying promiscuously 




Fig. 80. 



''^>'>m^M^ 



§ 309] MAGNETISM 181 

without any special arrangement, the body is demagnet- 
ized. Figures 80 and 81 show, diagrammatically, the 
supposed arrangement of molecules in magnetized and 
unmagnetized steel or iron. The 
effect of arrangement may be 
illustrated by picking up a nail 
with the north pole of a magnet, 

and then slipping a south pole along over the north, as 
shown in Fig. 82. If the magnets are of nearly equal 
strength, the nail will drop as the south pole comes over 
the north pole. On the contrary, if two north poles are 
brought together, the two will pick up more nails than 

— — 1 ^^^ ^Yi\\. Another experiment 

1^ ^^ s ] which illustrates this is to take 

a large number of very small 
Fig. 82. magnets and lay them together 

in a line, several deep, wide, 
and long, with their north poles all in one direction. It 



: 1 x . 






''0-^Mf- 


-J-';\;^ 


t'y 


11111 


; -v 


■^:--.-^^ 


V>,;». 


■■:j;:^^:.i:'-- 




V- -'-a 


im%mm 




- - -.x->: 


N 


■ '-■ "■ ; . ?:;- 


-- -- ■ 




% Wimi 




•;'.--- :>^;. 




-.: ■' -x , ^ 






'.'■-'. ■ , -^".■:i-^;■? 


/'.<■ 


'■^'r'r'^^ 








■~ 




'%■ - 


« 






T-yi- ■■ 




" \'_ 


•?--^ -.'•■■■:■ 




V'v'\ ■■-■'■""""--■ ^'^ 


r;:-:-^'- 


■/' /' 





Fig. 83. 



will be found that the whole mass will act as a strong 
magnet ; while, if the magnets are mixed up, or the 



182 



ELECTRICITY 



[§§ 309-310 



units are laid alternately, the mass shows little or no sign 

of magnetism. 



':■■' 310. Magnetic 

Fields. — Lay a 
::..; bar magnet upon 

the table, and 
V";'" ^^ over it a sheet of 
white cardboard. 
Sprinkle fine iron 
filings evenly over 
the cardboard, 
and jar the table 
slightly to assist in getting the filings into the position 
which they seem naturally to take. An arrangement like 
Fig. 83 will be obtained. These lines marked by the 
filings are called l{7ies of force, and the whole series the 
magnetic field of the magnet. The stronger the magnet 
the greater the number of lines of force, and the more 
clearly marked the field. If a compass be placed any- 
where in the field, it will be found that the needle stands 




Fig. 84. 




TCv^-9--": 



>\> 



x^C 



^>§^ 



•>^-'^ 






Fig. 85. 



parallel to the lines of force. It is an important fact to 
remember that a magnetic needle always tends to place itself 
parallel to lines of magnetic force. 



§§ 310-312] 



MAGNETISM 



183 




Fig. 86. 



If we lay two north poles toward each other and about 
an inch and a half apart, we get a field such as is shown in 
Fior. 84, which shows the action 
of like poles upon each other. 
In Fig. 85 we have the field 
between unlike poles, where the 
lines of force go directly from 
one pole to the opposite, and the 
poles attract each other. 

The lines of force are sup- 
posed to go from S to iV through 
the magnet, and from iVto S in the field, as shown in Fig. 86. 

311. The Dipping Needle. — If a piece of unmagnetized 
steel be suspended, and carefully balanced, so that it can 
move easily in all directions, it will be found that, if it 
is now magnetized, it will no longer balance, but the north 
pole will point downward at an angle which varies with 
the latitude. At the equator its position will be nearly 
parallel to the surface of the earth, while the farther north 
it is carried the more the north pole will be depressed. 

Comparing this with the directions which a needle takes 
when placed in various positions with reference to a 
strong magnet leads us to believe that the earth is a great 
magnet, and is surrounded by a magnetic field similar to 
that of a bar magnet, the poles, however, not being in the 
same position as the geographical poles of the earth. 

312. Permeability. — As has been indicated, the strength 
of a magnet is determined by the number of lines of force 
emanating from its poles, and, consequently, by the num- 
ber of lines of force which pass through the magnet it- 
self. It is found that some kinds of iron are capable of 
carrying more lines of force, and attract more than others. 
This property is called permeabiUty, and will be mentioned 
again in the discussion of electromagnets. 



184 ELECTRICITY [§§ 313-314 

SECTION 2. STATIC ELECTRICITY 

313. Electric Attraction. — Suspend a small ball of corn 
or sunflower pith by means of a silk thread, and bring 
first a glass rod and then a vulcanite rod near it. It will 
be found that the ball is neither attracted nor repelled. 
Now rub the glass rod with a piece of silk, and again 
bring it near, but so that the ball cannot touch it, and 
it will be found that the ball will be attracted. Re- 
peat with the vulcanite rod, after rubbing it briskly 
with flannel, and the same result will be obtained. A 
piece of silk ribbon held close to the wall is in no way 
attracted to the wall, but, if it is drawn two or three 
times through the folds of a piece of flannel, it will then 
adhere to the wall and stick there for some time. These 
simple experiments show plainly that the rubbing has 
imparted some property or force to the substance rubbed, 
which it did not at first possess. This property is called 
static^ or frictional^ electricity^ and the force is electric 
attraction, 

Thales, a Greek scholar, about 600 B.C., discovered that 
when amber was rubbed it would attract light substances, 
and, of course, the ancients knew something of lightning ; 
but the two were not in any way connected in their minds ; 
and for many centuries the one fact discovered by Thales 
was all that was known of static electricity. 

We are now very familiar with the things which elec- 
tricity will do, and how it acts under different conditions ; 
but as to its real nature we still know little or nothing, 
although many theories have been advanced. 

314. Two Kinds of Electric Charges. — Suspend a wire 
stirrup from some convenient support by means of a nar- 
row silk ribbon, and rub a glass rod with silk and place it 
in the stirrup, as shown in Fig. 87. Then rub the end of 



§314] STATIC ELECTRICITY 185 

another glass rod with silk, and bring this end near the 

rubbed end of the first rod. It will be found that the 

suspended rod will be repelled. Now rub a vulcanite rod 

with flannel and bring it near the suspended 

rod, and they will attract each other. If 

two vulcanite rods are used, they will repel. A 

An unrubbed or neutral rod of any kind will ' 

be attracted by either the rubbed vulcanite 

or the glass rod. p^^ g^_ 

These facts indicate that there are two 
kinds of electric charges. We call the charge generated 
upon the glass rod when rubbed with silk a positive, or 
+ , charge, and the charge upon a rubber, or vulcanite, 
rod, when rubbed with flannel, a negative, or — , charge. 

The amount of attraction is found to be less as the 
distance increases. If the distance between two charges 
is doubled, the attraction is found to be only one-fourth 
what it was at first. Doubling one of the charges, without 
changing the distance, is found to double the attraction, 
or repulsion, between the charges. 

These facts give rise to the following laws : 

Like charges of electricity repel each other, and unlike 
charges attract. 

The mutual action of two charges of static electricity upon 
each other is directly proportional to the product of the charges 
and inversely proportional to the square of the distance between 
them. 

The latter law may be put in the form of an equation ; 

Cc 
thus F = — — , in which C and c represent the respective 

magnitudes of the charges, and D the distance between 
them. 

We might also add a law : Neutral bodies are attracted by 
either a positive or a negative charge. 



186 ELECTIUCITY [§§ 315-316 

315. Charging by Contact. The Proof -plane. — A proof- 
plane (Fig. 88) is a metal disk, with its edges rounded off, 

and fastened to the end of a glass or vulcanite rod, 

usually by means of sealing-wax. Charge a rubber 

rod, and roll or rub it over the surface of the proof- 

^ plane ; then bring the plane near some sawdust or 

cork filings, and the light particles will be attracted, 

showing that electricity has been transferred from the rod 

to the proof-plane. This is called charging hy contact. 

Another good example of electrillcation by contact is to 
take a pith-ball, suspended by means of a silk thread, and 
allow it to touch a charged rod. It will adhere for a 
moment, and then be forcibly repelled, showing that the 
ball has become charged like the rod and then repelled. 

316. Electrostatic Induction. — Charge a pith-ball by con- 
tact with a glass rod, and it will then be repelled by the 
glass, but will be attracted by a rubber rod. Secure a 
metal cylinder with rounded ends, or a wooden cylinder 
covered with tin-foil, and mounted upon a glass or rubber 
rod, as shown in Fig. 89. Bring a positively charged rod 
near one end, as shown, and the 
cylinder will have two charges 
upon it, as indicated by the -f and 
— signs. This fact may be proven 
in the following way : Charge a 
pith-ball positively by contact with 
a glass rod, and suspend it, by 
means of a silk thread, near the + 
end of the cylinder, and it will 
be repelled; but lift it up and 

bring it over near the other end, without touching, and 
it will be found that this end of the cylinder attracts the 
positively charged pith-ball. 

If the charged rod, the charge of which is called the in- 




§§ 316-317] STATIC ELECTRICITY 187 

duciiig charge, is removed, the cylinder instantly becomes 
neutral again, leading us to believe that equal opposite 
charges neutralize each other when they come together. If, 
however, we hold the charged rod in place, and, while hold- 
ing it, touch the cylinder, thus connecting it with the earth, 
then remove first the finger and then the inducing charge, 
it will be found that the cylinder is charged all over with 
a charge opposite to the inducing charge. We call this 
process charging hy induction^ and the induced charge is 
always the opposite of the inducing. The charge that is 
attracted to the inducing charge and held is sometimes 
called a bound charge, and it will remain bound as long 
as the inducing charge is held in position, no matter what 
is done with the cylinder in the meantime. 

This electric separation explains why a neutral body is 
attracted by either a positive or a negative charge. The 
bound charge is nearer the attracting charge than the 
other ; and thus, as the attraction or repulsion is inversely 
proportional to the square of the distance, the attraction 
for the nearer charge is greater than the repulsion for the 
farther, and the body containing the charges is attracted 
with a force equal to the difference between the attraction 
of the opposite charges and the repulsion of the like charges. 

317. The Electrophorus. — Figure 90, A^ B^ and C, shows 
diagrams of the electrophorus. The plate, or base, p^ is a 
vulcanite disk, or a shallow pan of metal or wood, filled 
with a mixture of resin n 

and shellac or sealing- fl A If 

wax, and tlie cover <? |( if - ^^^"^^^2^ 

is a metal disk with ^-, ^}lliii lL^ ,. 'ttt't t"_^^ ^ ^ 

rounded edges, or a '^ ^ ^ 

disk of wood covered ^^' ' 

with tin foil, and provided with a glass or vulcanite 
handle. The plate is charged by rubbing with flannel 



188 ELECTRICITY [§§ 317-318 

or cat's fur, and has a — charge. When the cover is laid 
upon the plate it touches only a few places, and so is, 
practically, separated from the plate by a thin layer of 
air. The — charge upon the plate acts inductively upon 
the cover, and produces the condition shown in A. 
Now touch the cover c with the finger, and the free — 
charge will be conveyed to the earth, and the + charge left 
bound as shown in B. Then when the cover is removed, 
as in (7, the + charge will be free, and will be distributed 
over the whole surface of the cover. 

In this way the cover may be charged a number of times 
without recharging the plate ; and it appears at first sight 
as if we were creating energy ; for each charge upon the 
cover represents a definite amount of energy, and we get 
it without recharging the plate. But the cover lifts harder 
when so charged than when not, and the difference between 
the energy required to raise it when charged and when 
not charged, is just equal to the energy stored in the 
charge upon the cover. So the energy of the charge upon 
the cover is not derived from the charge on the plate, but 
from the energy required to separate the two opposite 
charges after the — charge has gone to the earth. 

318. The Gold-leaf Electroscope. — An electroscope is an 
instrument for the detection of the presence and nature of 
a charge of electricity. The most sensitive and satisfac- 
/-^ tor}^ form is the gold-leaf electroscope shown 

in Fig. 91 ; although a light pith-ball, sus- 
pended by means of a silk thread, is very 
good. The gold-leaf electroscope consists 
of a small rod H bent at right angles at one 
end, with a metal ball or disk at the upper 
end, and a pair of gold-foil leaves suspended 
from the bent end as shown in the figure, the 
Fig. di. whole being placed in a flask or bottle to 





§§318-319]' STATIC ELECTRICITY 189 

protect the leaves from moisture and drafts. The rod 
should pass through a rubber stopper or a thick glass 
tube pushed through a common cork. 

If a charged glass rod is brought slowly near the knob, 
the leaves will separate ; and a little reflection will make 
it clear that the inductive action of the rod 
will cause the arrangement of charges 
shown in Fig. 92, as the leaves will be 
charged alike and so will repel each other. 
When the charged rod is removed, the 
leaves droi:) together because of their own 
iveight., but are never attracted to each other. 

Bring the rod in contact with the ball 
and the leaves will remain apart when the 
rod is removed ; but bring an oppositely 
charged rod sloivly near, and the leaves will 
drop together, because the charge upon them is drawn to 
the ball and they are left neutral. 

Now bring the + charge six or eight inches above the 
ball, and while holding it in position, touch the ball with 
the finger and the leaves will drop together. Remove first 
the finger, and the leaves will separate ; remove then the 
rod, and the leaves will first drop together and then sepa- 
rate and remain so. If a + charge is brought near, they 
will drop together, but if a — charge is brought near the 
ball, the leaves will separate more strongly, showing that 
the charge induced in the leaves is opposite to the inducing 
charge. Thus the instrument very readily show^s the 
presence and nature of a static charge. 

319. Inductive Capacity. Dielectrics. — The amount of 
electricity which can be induced into an insulated con- 
ductor depends upon the strength of the inducing charge, 
the area of the surface of the body, and the nature of the 
substance in the intervening space. A substance through 



190 



ELECTRICITY 



[§§ 319-320 



wliicli inductive action will take place is called a dielec- 
tric, and air is taken as the standard. It is found that a 
dielectric between two opposite charges is in a strained 
condition, and if the charges are strong enough the dielec- 
tric will be pierced and a spark will pass. If a charged 
rod be brought near the ball of an electroscope, and held 
stationary, a certain amount of deflection of the leaves is 
produced ; and if a block of paraffine or plate of hard 
rubber be placed between, the repulsion of the leaves is 
increased, showing that the paraffine or rubber is a better 
dielectric than air. The following table shows the specific 
inductive capacity of some of the best dielectrics : 

Air 1.00 Shellac .... 2.75 

Paraffine . . 2.00 Ebonite. . . . 3.40 
Rubber ... 2.25 Glass 6.25 

This is only approximate, however ; different grades of 
glass, for instance, vary greatly. 

320. Position and Distribution of a Charge. — Experiment 
shows that a static charge rests upon the surface of a con- 
ductor, and if the conductor is a sphere, the charge is 
distributed equally over the surface. But if 
the conductor is shaped as shown in Fig. 93, 
the charge is unevenly distributed, and has the 
greatest density at the more pointed end. 
Charge a metal cylinder, ar- 
ranged as in Fig. 94, with a 
pair of pith-balls suspended in- 
side, and another pair outside, 
by means of a linen thread, 
with the whole mounted upon 
a glass or rubber rod, and it will be found that the 
balls suspended upon the rod on the outside become 
charged and repel each other, while the ones on the inside 





Fig. 93. 



Fig. 94. 



§§ 320-321] STATIC ELECTRICITY 191 

remain perfectly neutral. A proof-plane brought in con- 
tact with the outside becomes charged, while if placed 
against the inner surface it remains uncharged. 

In case of the egg-shaped conductor (Fig. 93), it will 
be found that a proof-plane applied to the pointed end 
will receive a much stronger charge than if applied 
anywhere else, and a stronger charge at the larger 
end than at the middle of the side. We may say, then, 
that there is a strong tendency for a charge to collect 
at points. 

321. Pointed Conductors and Convective Discharge. — As 
the electricity gathers at projecting points of a conductor, 
the shorter the radius of curvature the greater the elec- 
trical density ; and at sharp points we find a very great 
amount of electricity compared to that found on other 
surfaces. If we charge a large insulated con- 
ductor, a cylinder with rounded ends, or a 
sphere, a pair of pith-balls suspended together 
from the conductor by linen thread will repel 
each other and remain apart for a long time ; 
but if a wire, with several points attached, is 
placed upon the conductor, as shown in Fig. 95, 
the balls will very soon drop together, showing 
that the charge has escaped. Moisten the hand 
and hold it in front of the points, and a current of air 
can be felt coming from them. A candle held in front 
of a single point can often be blown out. If a person 
stands upon an insulating stool, close in front of the 
points, for a few moments, it will be found that his body 
has become charged, and that sparks will pass from his 
hand to any one standing near. 

We have seen pith-balls attracted to a charged rod, and 
then repelled after receiving a charge like the rod. Now, 
what happens in the case of the pointed conductors is 




192 



ELECTRICITY 



[§§ 321-323 







:T;r 



much the same : the molecules of air correspond to the 
pith-balls, and are attracted to the point and then are 
repelled straight from the point which is the most highly 
charged, while neutral molecules from all sides are at- 
tracted in turn ; the result being a current of air moving 
from the point, each molecule in the stream carrying a 
minute charge of electricity, to be given up wholly or in 
part to the first neutral or oppositely charged body with 

which it comes in con- 
tact. Such a discharge 
is called convective. 

322. Electric Machines. 
— There are two forms 
of electric machines for 
generating static electri- 
city in common use ; they 
are the frictional and the 
induction machines. A 
common form of the in- 
duction machine is the Toepler-Holtz, shown in Fig. 96. 
The action is somewhat complicated, and no explanation 
will be given here. 

323. Potential. — The electrical potential of a body is 
its condition with regard to its ability to give up elec- 
tricity to other bodies, a passage of electricity always 
taking place from the body of higher to the body of lower 
potential. We found in the study of lieat that a small 
body of high temperature might contain much less heat 
energy than a larger body of much lower temperature. So 
a small conductor may have a much higher potential with 
a small charge of static electricity than a larger body 
which contains a much larger charge ; and if the two were 
brought in contact, there would be a passage of electricity 
from the small to the large conductor, as heat passes from 



Fig. 96. 



§§323-324] STATIC ELECTRICITY 193 

a small body with a liigli temperature to a large body with 
a lower temperature. 

If, for instance, a ball having an area of 1 cm.^ has a 
charge of 5 units, and another body with an area of 30 
cm. 2 has a charge of 15 units, the smaller body will have 
much the higher potential ; and a spark will pass a wider 
gap from it than from the other. But if a spark were to 
pass from the larger, it would carry with it a larger charge, 
although it would not jump so far. 

324. Condensers. — Let two conductors be placed near 
each other, with some dielectric between them, one con- 
nected with the earth and the other with some source of 
static electricity, as shown in Fig. 97, where A and B 
are thin plates of metal, and (7 is a plate 
of glass. Such an apparatus is called a 
condenser. B is connected with the + 
pole of an electric machine, and A is con- 
nected with the earth by means of a wire 
or chain. Now, if B is charged with + 
electricity it will readily be seen that the 
+ charge will act inductively through 
the glass, and that a — charge will be ^^' 

induced and bound upon A. More and more + can be 
added to 5, and more and more — will be drawn to and 
bound upon A until the potential of the charge upon B is 
equal to the potential of the charge from the source. 

If, now, one end of a conductor is placed in contact 
with one plate, and the other end brought near the other 
plate, a spark will pass ; and then both plates will be found 
to be neutral. If the distance between the plates is great, 
the charge induced upon A Avill not be so great as if they 
are close together, because the mutual attraction between 
two opposite charges is inversely proportional to the 
square of the distance. The charge depends also upon 




194 ELECTRICITY [§§ 324-326 

the inductive capacity of the dielectric used. It will 
readily be seen that the reciprocal inductive action of 
the plates A and B upon each other will cause them to 
contain a much greater charge than either would by itself. 
In order to construct the best possible condenser, a 
dielectric with the highest possible specific inductive 
capacity is desirable, and this must be as thin as is possible 
without its being pierced by the strain which the attrac- 
tion of the opposite charges places upon it. 

325. The Leyden Jar. — The Leyden jar (Fig. 98) is one 
form of condenser, and is simply a thin glass jar coated 

04. about two-thirds of the way up, both inside and 
^^ out, with tin-foil, connection being made with 
^^^ the inner coating by means of a knob and rod, 
to the lower end of which is attached a small 
chain or spring which rests upon the bottom of 
the jar. To charge the jar hold it in 
^^' * the hand, thus connecting the outer 
coating with the earth, and place the knob near, 
or in contact with, the pole of an electric machine. 
To discharge, place one end of a discharger 
(Fig. 99) against the outer coating, and bring 
the other end slowly toward the knob of the jar, when 
a spark will pass. 

326. Position of the Charge. — If, a moment after the 
discharge of a Leyden jar, we again apply the discharger, 
we shall get another, but much smaller, spark. This 
would lead us to think that the charge does not rest upon 
the metal coatings, for in that case a complete discharge 
would take place at once, as in the case of other metallic 
conductors. The fact that the glass is sometimes broken 
shows tliat it is under a stress, and that the residual dis- 
charge probably comes from the gradual return of the 
strained molecules to their normal condition. 



U 




§§ 32G-328] 



STATIC ELECTRICITY 



195 





If a jar made with movable coatings (Fig. 100) is 
charged, and the coatings removed and placed together, so 
there can be no possible doubt of their being discharged 
(if either contained any charge), it will be 
found upon replacing the coatings, or replacing 
them with similar ones, that the jar still con- 
tains as strong, or nearly as strong, a charge 
as when first charged. This shows conclusively 
that the charge rests upon the glass and not 
upon the metal coatings, and that the coatings 
are useful only in distributing the charge over 
the surface of the dielectric in charging the jar 
and conducting it away in discharging. 

327. Atmospheric Electricity. — The similarity 
in the appearance of a long spark from an elec- 
tric machine and a flash of lightning is very 
noticeable, and the identity of the two had been 
suspected ; but it was left to Benjamin Franklin 
to prove, when, with his famous kite experi- 
ment in 1752, he charged a Leyden jar by 
electricity conducted down a wet kite string, 
thunder-storm arises, the clouds become charged ; and this 
charge upon the clouds acts inductively upon the earth, 
inducing an opposite charge on the surface directly beneath, 
and we thus have a great condenser in which the cloud is 
one plate, the earth the other, and the intervening air the 
dielectric. When the charge becomes powerful enough, a 
great spark which we call lightning passes between the two. 

328. The Lightning-rod. — A metal rod placed upon a 
building, with its lower end terminating below the surface 
of the ground where it is always wet, and the upper end 
of the rod terminating in a number of sharp points, is 
often used as a protection against lightning ; and in some 
cases a flash of lightning may follow such a rod to the 




Fig. 100. 

means of 
When a 



196 



ELECTBICITY 



[§ 328 



/ 



Fig. 101. 



ground as the path of least resistance ; but the work that 
a lightning-rod should do is to discharge any approaching 
cloud by convective discharge. If the 
--z^^ ^ - " hand is held in front of the points 

of a lightning-rod during a thunder- 
storm, it will be found that there is 
a strong current of air passing from 
each point. Figure 101 represents the 
conditions in such a case. The posi- 
tively charged cloud induces a nega- 
tive charge in the earth beneath, and, 
of course, the — electricity is attracted 
to the points of the rod nearest the 
cloud, and surrounding molecules of 
air are attracted, charged, and repelled 
toward the cloud. If this process could 
go on long enough, the cloud would be entirely discharged, 
or neutralized. 

The points upon the ordinary lightning-rod are entirely 
insufficient to do this, and the result is that the average 
lightning-rod is fully as much a menace as a protection, for 
it reaches above the building so that it tends to draw the 
discharge, without having the capacity to carry it if it 
strikes. Many cases are on record where the lightning 
has struck a rod, and jumped from that to the building, 
doing as much damage as if the rod had not been there ; 
and very probably it would not have struck at all if the 
rod had not been there. 

A large number of points, as might be obtained by the 
stringing of a quantity of barbed wire, would no doubt 
prove some practical protection to a building ; and, with 
proper arrangement, the neighborhood of a barbed-wire 
fence might no doubt be made the safest place for stock 
during a thunder-storm. 



Cattle and horses are often 



§§ 328-330] VOLTAIC ELECTRICITY 197 

struck by lightning when standing near such fences as 
they are ordinarily constructed, and this is no doubt be- 
cause the wire attracts the lightning but offers no path 
to the earth through the dry posts ; so it passes to the 
bodies of animals standing near, and thus to the earth. 
This might be avoided by attaching cross-wires to the 
fence wires and running these cross-wires down into the 
moist earth at frequent intervals along the fence, thus 
giving ample opportunity for convective discharge, and, 
in case of a bolt of lightning striking the fence, a good 
path for it to follow in passing to the earth. 

SECTION 3. VOLTAIC ELECTRICITY 

329. Electric Currents. — We have already found that 
if two bodies of different potentials are brought in contact, 
or are connected by a conductor, they neutralize each 
other,, as there is a flow of electricity, or an electric cur- 
rent^ between the two. Careful tests show that the in- 
stant the conductor touches the two bodies, some change 
takes place in the condition of the conductor and the im- 
mediate vicinity. For convenience, we say that the flow 
of the discharge is from positive to negative^ if the bodies 
are differently charged, or, if similarly charged, from high 
to low potential. In the case of bodies charged with 
static electricity, it takes but an instant to neutralize the 
bodies ; but suppose that, by some means, the potential of 
each could be kept constant, there would then be a con- 
stant flow as long as the bodies were connected by the con- 
ductor ; and it will readily be seen that the greater the 
difference of potential, the greater the amount of electricity 
that will flow in a given time. 

330. The Voltaic Cell. —In 1792 Volta discovered a 
method of producing a constant difference of potential, 




198 ELECTRICITY [§§ 330-331 

and thus a constant flow, of electricity. The apparatus 
used is called a voltaic cell^ and it consists of two metal 
plates, usually one copper and one zinc, with a piece of cop- 
per wire soldered, or otherwise fastened, to the end of each 
plate. The plates are then set into a jar of dilute sul- 
phuric acid (H2SO4), prepared by pouring one part of the 
acid into ten parts of water. If the plates are set into 
the dilute acid, or exciting fluid as it is 
called, and the attached wires are left apart, 
it will be seen that bubbles gather and rise 
around the zinc plate. Now, if the ends 
of the wires are twisted together or fastened 
by means of a connector, the bubbles will 
gather upon the copper plate instead, and 
a change takes place in the condition of 
the wire, as Ave shall show later. 

Figure 102 shows a simple voltaic cell. These are fre- 
quently called galvanic cells. A battery consists of two 
or more cells connected together. 

331. Poles of a Cell. — If the wires attached to the plates 
of a cell are connected for some time, it will be found that 
the zinc is wasting away; and an analysis of the fluid 
shows that a chemical change is taking place, zinc sulphate 
being formed and hydrogen being liberated. Zinc -{- sul- 
phuric acid forms zinc sulphate + hydrogen ; or, the chem- 
ical reaction is as follows : Zn + H2SO4 =ZnS04 + ^2- 

The chemical action upon the zinc seems to be the cause 
of the flow of the current through the wire. As the 
action is upon the zinc, we call the zinc the positive plate ; 
and the copper, which is acted upon little or none, is called 
the negative plate. The current, then, is said to flow from 
the zinc to the copper plate in the cell through the excit- 
ing fluid, and then, of course, it must flow from the copper 
to the zinc through the wires which we call the external 



VOLTAIC ELECTRICITY 199 

circuit. So, for convenience, we call the top of the nega- 
tive plate, or the end of the wire attached to it, the positive 
pole^ or electrode^ and the corresponding part of the posi- 
tive plate the negative pole^ or electrode, so that every- 
where the current flows from positive to negative^ or from 
+ to - . 

332. Test for Presence and Direction of a Current. — 
Remove the zinc plate from the exciting fluid, and bring 
the connecting wire down over, and parallel to, the needle 
of a compass, and it will have no effect upon the needle ; 
but place the plate in the fluid, and the needle is at once 
deflected from a north and south position, showing that 
there is some force in or around the wire which was not 
there before. This is one of the common tests for the 
presence of a current of electricity in a conductor. We 
have assumed for convenience that the current flows from 
-}- to — ; and if the right hand is placed over the wire, 
with the palm toward the needle, and the fingers pointing 
in the direction of the current, as if the hand were floating 
in the current with the fingers forward, the thumb will 
be on the side of, or point toward, the deflection of the 
north-seeking pole. 

If, then, we have a conductor which we wish to test, we 
may stretch a portion of it in a north and south direction, 
and bring a compass-needle under it. If there is a deflec- 
tion of the needle, there is a current in the wire ; and to 
determine its direction, hold the right hand as directed 
above, with the thumb pointing in the direction of the 
deflection of the north-seeking pole, and the fingers will 
point in the direction of the flow. This principle is 
made use of in the construction of the galvanometer, as 
we shall see later. 

333. Closed and Open Circuits. — When the poles of a 
battery are connected by means of a conductor, we say 



200 ELECTRICITY [§§ 333-334 

that we have a closed circuit; but when there is a break 
anywhere in the circuit, the current ceases to flow, and we 

say that we have an open circuit. 
r ": T ■ -.vy/y ///>A ^~ Ouc of the commou devices for opening 



.B 



and closing a circuit is a contact key (Fig. 

103), in which (7 is a brass spring, the base 
B is some insulating material, and the wires are connected 
at A and D. When the spring is pushed down, a con- 
tact is made at Z>, and we have a closed circuit ; but as 
soon as O is released, it flies up, the circuit is broken, and 
we have an open circuit. 

334. Cause of Difference of Potential. ^ — The difference 
of potential between the plates of a voltaic cell seems to 
be due to the difference of chemical action upon the two 
plates. If two plates of the same material are used, there 
will be no current generated ; but if different plates are 
used, we get a flow of electricity, and the greater the differ- 
ence of chemical action^ the stronger the flow. If we use 
copper and iron plates, we get a certain difference of 
potential, and the flow is from the copper to the iron 
through the wire connecting them ; if we use iron and 
zinc, we get a flow from the iron to the zinc ; and if w^e use 
copper and zinc, we get a much greater difference of 
potential than in either of the other cases, and the flow is 
from the copper to the zinc. The zinc is acted upon most 
readily by the acid, the iron much less, and the copper 
practically not at all. 

We conclude, then, that the chemical action upon the 
active plate raises its potential, causing a flow from that 
plate to the other through the exciting fluids thus raising 
the potential of the pole attached to the other plate. 
Chemical action is one form of energy ; and we have this 
form here transformed into another which we call electri- 
cal energy. 




VOLTAIC ELECTBICITY 201 

335. Polarization and Local Action. — If the zinc plate is 
pure, and the circuit is open, the acid acts upon tlie zinc 
until a coating of hydrogen gathers upon the surface, when 
the action is checked to a greater or less extent ; but when 
the circuit is closed, the hydrogen gathers upon, and is 
evolved from, the copper plate ; and when the cell described 
above is used, it will be noticed that, when the surface of 
the copper plate is covered with hydrogen, the current 
strength is greatly diminished. This condition is called 
polarization. The diminution in the strength of the cur- 
rent is due to two things : first, to the resistance of the 
hydrogen coating to the passage of the current; and, 
second, to a tendency of the hydrogen upon the copper 
plate to set up a current in the opposite direction. 

When impure zinc is used, such as we ordinarily get for 
commercial purposes, the action goes on much the same 
whether the circuit is closed or open, as the bits of impuri- 
ties in the zinc act as negative plates, and little local 
circuits are formed between these and the zinc ; hence only 
a small portion of the chemical energy represented by the 
oxidation of the zinc is converted into available electrical 
energy. This phenomenon is called local action. 

Polarization is avoided by putting some substance into 
the exciting fluid which will combine with the hydrogen 
and thus remove it, or by roughening the surface of the 
negative plate so that the hydrogen will rise to the surface 
as fast as it is formed. The substance used is generally 
one which will oxidize the hydrogen and form HgO, or 
water. 

The remedy for local action is to amalgamate the zinc 
by coating its surface with mercury. This may easily be 
done by simply placing the zinc in the acid for a moment, 
and then rubbing mercury over the surface. When thus 
amalgamated, the surface is composed of an amalgam, or 



202 ELECTRICITY [§§ 335-337 

alloy, of mercury and zinc, covering over the impurities ; 
so the acid comes in contact with only the zinc and the 
mercury, which forms a smooth surface to which the 
hydrogen clings. 

336. Forms of Cells. — There have been many forms of 
cells devised to get rid of polarization, and to give as 
strong and constant a current as possible. For some kinds 
of work the circuit may be kept open when not in actual 
use, but in others the circuit must be kept closed, and a 
cell which will work admirably in one case may be useless 
in the other ; so the form of the cell must be adapted to 
the work that is to be done. 

337- The Gravity Cell. — A gravity cell is shown in Fig. 
104. It is made up of a negative plate consisting of three 
plates of copper riveted together in the middle and spread 
out so as to cover the bottom of the jar. This is connected 
with the external circuit by means of a wire covered with 
rubber. The positive element is a crowfoot-shaped piece 
of zinc, hung in the upper part of the jar, as 
shown. The copper plate is covered with copper 
sulphate crystals (CuSO^), and the jar is then 
filled with very dilute sulphuric acid (HgSO^). 
When the circuit is completed, the acid acts 
upon the zinc, forming zinc sulphate (ZnSO^) 
and hydrogen (H), the chemical change being 
represented by the following reaction : Zn -f- HgSO^ = 
ZnSO^ + H2. The hydrogen passes toward the copper 
and displaces some of the copper in the CuSO^, the copper 
is deposited upon the copper plate, and the hydrogen 
forms with the CuSO^ more HgSO^, which in turn dis- 
solves more of the zinc. The reaction between the H and 
the CuSO^ is : Hg + CuSO^ = H2SO4 + Cu. Thus the 
zinc wastes away, and the copper plate grows heavier, and 
there is a constant formation of zinc sulphate. The zinc 




§§ 337-339] VOLTAIC ELECTRICITY 203 

sulphate is somewhat lighter, and hence is buoyed up by the 
copper sulphate ; and when the cell is working properly, 
the two remain clearly separated, the zinc above the 
copper. 

This cell must be kept in closed circuit. It gives a very 
constant current, as it never becomes polarized ; but the 
current is not very strong. It is used principally in 
telegraphy. 

338. The Bichromate Cell. — ■ The potassium or sodium 
bichromate cell consists of a zinc plate hung between two 
plates of carbon, the latter being used for negative plates 
instead of copper. The fluid is a lOfo solution of sul- 
phuric acid, in which is dissolved one pound of potas- 
sium or sodium bichromate to the gallon ; chromic acid is 
frequently used instead. A little nitric acid, or sodium 
nitrate, added to this solution helps to keep the cell from 
polarizing. This cell gives a strong, and fairly constant, 
current ; although it gradually grows weaker as it is used. 
The zinc plate wastes away almost as fast when the circuit 
is open as when closed ; so the cell is so made that the zinc 
plate may be lifted out of the fluid when it is not in use. 

339. The Leclanche Cell. — One of the commonest forms 
of the voltaic cell is the Leclanche (Fig. 105). It is used 
for open-circuit work where a fairly strong current may be 
wanted for a short time at any moment for ring- 
ing bells and so forth. The elements are a rod 
of zinc and a plate of carbon, the latter placed 
in a porous cup which is filled with bits of carbon 
and manganese dioxide. The exciting fluid is 
a saturate solution of ammonium chloride (sal 
ammoniac). One of these cells, when properly 
put up, will remain in good working condition ^^' ^' 
for months, giving a current for a few seconds at a time ; 
but it becomes polarized very quickly. However, the hydro- 




204 ELECTRICITY [§§ 339-341 

gen, which causes the polarization, is soon oxidized by the 
oxygen in the manganese dioxide, and forms water. 

340. Use of Voltaic Cells and Batteries. — ■ The practical 
use of voltaic cells is very extensive, notwithstanding the 
fact that the current generated by such cells is far 
more expensive, proportionately, than those generated by 
dynamos. Cells are used, however, where small quantities 
of electric energy are required, because of the slight 
original cost, the little care required, the small space 
occupied, or the lowness of the voltage. The voltage 
required by many electric apparatuses ranges from one 
to ten volts ; and, as the voltage of a cell is usually about 
one volt, it is a simple matter, by proper connections, to 
secure any low voltage with a battery of a few cells. 

Voltaic cells are used almost exclusively for electric bells, 
for the smaller telephone and telegraph systems, and for 
running innumerable small contrivances, especially those 
requiring current intermittently, or of low voltage. They 
are of great value in carrying on many investigations in 
science, particularly where very low but constant currents 
are required. 

SECTION 4. ELECTRIC CURRENTS 

341. Electromotive Force. — If two tanks filled with 
water are set at different levels, and connected by means 
of a pipe, there will be a flow of water from the higher to 
tlie lower tank, and the water pressure will be propor- 
tional to the difference of level of the two water surfaces. 
In a similar way when plates of a cell having different 
potentials are connected by means of conductors, there 
will be what we call electrical pressure, or electromotive 
force (E.M.F.), a form of force which causes the condi- 
tions which we call an electric current. The greater the 
difference of potential, the greater the E.M.F. 



§§ 341-343] ELECTRIC CURRENTS 205 

The voltaic cell may be compared to a force-pump, and 
the electrodes to tanks. The chemical action between the 
exciting fluid and the zinc is the force applied to the 
pump ; and for every unit of zinc dissolved, there is a defi- 
nite amount of electrical energy sent to the positive elec- 
trode when the circuit is closed ; and this tends to flow back 
through the external conductor to the negative electrode. 
The E.M.F. of a cell is determined by the nature of the 
materials used, and is independent of the size of the plates, 
just as the height to which water may be forced is indepen- 
dent of the sectional area of the pump. A large pump 
might throw a larger flow of water, but, with the same 
pressure to the square inch, would force it no higher. 

342. Volt. — The unit by which E.M.F. is measured is 
the volt. It is very nearly the pressure caused' by the 
difference of potential between the elements of a gravity 
cell. Because of the name of the unit, electromotive force 
is frequently called voltage. 

343. Resistance. — It is found that every conductor offers 
more or less resistance to the passage of a current of elec- 
tricity, just as a pipe offers more or less resistance to the 
flow of water through it. If a pipe is small, long, and 
rough inside, it will require more pressure to get a cer- 
tain amount of water through it in a given time than if it 
is large, short, and smooth. Similarly the resistance of 
a conductor depends upon its sectional area., its length., and 
the material of which it is made. Given a conductor of 
uniform material and size, and its resistance is directly 
proportional to its length : thus, if the length is doubled, 
the resistance will be doubled. Increased area of cross- 
section decreases the resistance proportionately. 

The laws of resistance are : The resistance of a conductor 
varies inversely as its sectional area or inversely as the 
square of its diameter. 



206 ELECTRICITY [§§343-346 

It varies directly as the length of the conductor. 

It varies as the material of which the conductor is made. 

344. Ohm. — The unit of resistance is the ohm. It is 
the resistance of 30 ft. of No. 25 copper wire, or of a col- 
umn of mercury at a temperature of 0° C, having a uni- 
form cross-section, a length of 106.3 cm., and a mass of 
14.4521 g. 

345. Determination of Resistance. — To determine the 
resistance of a conductor, we may apply the following 
equation : „ 

in which H is the resistance in ohms, K a constant which 
varies with different materials, I the length in feet, and D 
the diameter measured in mils, or thousandths of an inch. 
Various data in reference to copper wire are given at page 
374 ; and the sizes of wires are the same for any material 
if the number is the same. The circular mils referred to 
in the table are equal to the mils squared. The constants 
for some of the common conductors are given in the fol- 
lowing table : ^ . ^ 

Silver 9.53 Platinum .... 58.00 

Copper 10.35 Iron 63.00 

Aluminum . . . .19.00 German-silver . . 135.90 

These values are approximate, and vary somewhat with 
change of temperature, but will give no appreciable error 
at the ordinary temperature of the room. 

346. The Ampere. — The strength of a current, or its 
rate of flow, is measured in amperes. An E.M.F. of one 
volt, working through a resistance of one ohm, gives a 
flow of one ampere. If the electrodes of a battery are 
placed in a solution of a copper or silver salt, the elec- 
trodes being made of the metal contained in the salt, the 



§§ 346-349] ELECTRIC CURRENTS 207 

copper or silver will be deposited upon the negative elec- 
trode, or cathode^ at a rate which depends upon the strength 
of the current. If the flow is one ampere, .001118 g. of 
silver, or .000329 g. of copper, will be deposited each 
second. Because of the name of its unit, the strength of 
the current is frequently called the amperage. 

347. The Coulomb. — The coulomb is the electrical unit 
of quantity^ and is the amount of electrical energy which 
passes along a conductor in one second, when the pressure 
is one volt and the resistance of the conductor is one ohm. 
Or, it is the quantity of electricity which passes a point 
on a conductor in one second, when the current strength 
is one ampere. 

348. The Watt. — The watt is the unit used in the meas- 
urement of electrical poiver^ or the rate at which a current 
works. A current has a power of one watt when the 
pressure is one volt and the flow is one ampere. Hence, 
Watts equal volts times amperes. Thus, a current of 5 
amperes with a voltage of 6 has a power of 30 watts. 

One horse-power equals 746 watts. 

349. Ohm's Law. — Experiment proves that if a current 
is flowing through a circuit, and we increase the voltage, 
or E.M.F., without changing the circuit in any way, there 
will be an increase of flow proportional to the increase of 
E.M.F. On the other hand, if the E.M.F. remains 
constant, and the resistance of the circuit is increased, the 
flow of current will be proportionately decreased. Thus 
we have the following rule, which is called Ohm's Law : 

The strength of a current varies directly as the electromotive 
force and inversely as the resistance. 

The following formulas are common methods of express- 
ing the law : 

n E . Volts 

(J = — , or Amperes = — ■. 

R ^ Ohms 



208 ELECTRICITY [§§ 349-351 

It will readily be seen that if any two of these values are 
known, the third may be determined. 

350. Internal and External Resistance. — When a voltaic 
cell forms any part of an electric circuit, we must consider 
not only the resistance of the conductor which connects 
the electrodes of the cell, but also the resistance of the 
cell itself. The former is called external^ and the latter 
internal^ resistance. The current must flow through the 
exciting fluid, which is sometimes called a conductor of 
the second class ; and such conductors have a much higher 
resistance than metals or carbon, which are called conduc- 
tors of the first class. 

If the two plates of a cell have each an area of 10 cm. 2, 
and are placed 2 cm. apart, they are connected by a prism 
of the exciting fluid having a sectional area of 10 cm. ^ and 
a length of 2 cm. If, now, we move the plates 4 cm. 
apart, the length of the liquid prism will be doubled, and 
thus the resistance to the passage of the current will be 
doubled. On the other hand, if we double the size of the 
plates, we double the sectional area of the liquid prism, and 
make its resistance one-half as great. 

Thus we see that the same law holds for both kinds 
of conductors, and that the internal resistance of a cell 
is determined by the size and distance between the plates. 
It also depends, as with conductors of the first class, upon 
the nature of the conductor. As resistance anywhere in 
a circuit is a detriment, one thing to be sought for in the 
construction of a cell is a low internal resistance. 

351. Voltaic Batteries. — Two or more cells may be con- 
nected to work together, and then we have a voltaic battery. 
There are three general methods of connecting cells and 
almost an endless variety of combinations which may be 
made. The method of connecting is determined by the 
work which is to be done. 



352] 



ELECTRIC CURRENTS 



209 




352. Series Connection. — Figure 106 represents, in dia- 
gram, six cells connected in series, the heavy line representing 
the positive or zinc plate, the 
light line the negative plate, 

and the small arrow the direc- i~*f — H IH H M r 
tion of the current through ■^^^- ■^^^• 

the exciting fluid. In a battery of this kind the current is 
passed along from cell to coll in series, each cell adding its 
electromotive force as the current passes along. The result 
is that the voltage of such a battery is the voltage of a 
single cell times the number of cells in series. 

The action is something like that of a series of force- 
pumps set one above the other, with the discharge of one 
passing into the tank from which the 
next higher takes its supply, and so on, 
as indicated in Fig. 107. It is evident 
that only as much water will be passed 
along as the first pump is capable of 
raising, and it will be raised only to such 
height as the pressure on the piston will 
produce ; but the next pump will take 
this water and raise it to a greater height, 
and so on through the series. If the 
water must be pumped to a great height, 
and pumps capable of giving only a small 
pressure are to be obtained, some such 
arrangement as this is necessary. 

Now if w^e compare the water pressure 
at the outlets, p and p\ of the upper and 
lower tanks, it will also be evident that 
the pressure due to the upper tank is 
as many times that due to the lower as there are pumps 
in the system ; consequently, the resistance to be over- 
come by the water may be that many times greater. In 




t^J-Aau 



Fig. 107 



210 ELECTRICITY [§§ 352-353 

the same way, if a great resistance is to be overcome by 
an electric current, a high pressure is necessary. If voltaic 
cells are used, as the pressure or electromotive force of 
each is low, some such arrangement must be resorted to, 
to secure the required electromotive force, and connection 
in series is the usual method. 

The disadvantage of this arrangement is that, while it 
increases the voltage, it also increases the internal resist- 
ance of the battery, as the whole current must pass 
through the entire series, and thus the length of the liquid 
conductor is multiplied by the number of cells that are 
used. Consequently the internal resistance of a number 
of cells in series is the resistance of one of the cells times 
the number of cells. 

353. Multiple Connection. — Figure 108 shows six cells 

connected abreast, in multiple^ or parallel. In this case 

the voltage of the battery is the voltage of a single 

r \ cell ; the current is sent directly from each cell 

vLL> to the external circuit, and of course the pressure 

in the conductor cannot be higher than the press- 

H4^ ure of any cell which is sending out a current. 

Here again we may use the water analogy. 
Suppose a water-main (Fig. 109) is supplied by 
a pump having a maximum pressure of 10 lb. per 
Mi^ square inch. It is evident that when the pressure 

\ii/ in the main reaches an intensity 

^ of 10 lb. per square inch, the ^ — |f|_.f|_.f| — .f 
hack pressure will stop the ^ -' | '-^ 
action of the pump-piston. If, how- 
ever, the main is larsfe, and the water 

r. Ti T 1 • 11 Fig. 109. 

flows readily through it, and a large 
supply of water is needed, it is evident that it will be of 
advantage to start all of the pumps JL, B, C, and D, as the 
four will furnish four times as much water as one. 



\ 



§§353-355] ELECTIUC CURRENTS 211 

If, however, the water-main is almost closed, so that less 
water can flow than one pump can furnish, there is little 
or no advantage in having the four pumps, as the pumps 
will all stop as soon as the pressure in the main is equal to 
the maximum pressure of a single pump, and one pump 
would do the work as well as more. If, on the other 
hand, the pumps in such a case were connected in series^ 
the increased pressure would force more water through the 
small opening ; and this principle applies equally well to 
electric batteries. 

Hence, in general, we may say that, for high external 
resistance the series connection is the best, but for low 
external resistance, cells connected in parallel will give 
the best results. 

354. Multiple Series Connection. — Figure 110 shows six 
cells connected in multiple series, that is, two sets of three 
each connected in series, and the two sets 
connected in parallel. In this case the 
total voltage of the battery is the voltage 
of one of the sets of three which are con- 
nected in series, and the total resistance 
is the resistance of one of the sets divided ^^' 

hy the number of sets which are connected in parallel to 
make up the battery. 

355. Summary. — We may sum up these statements as 
follows : 

The E.M.F. of a battery in series is the E.M.F. of one 
of the cells times the number of cells. 

The internal resistance of a battery in series is the resist- 
ance of one of the cells times the number of cells. 

The E.M.F. of a battery in parallel is the E.M.F. of a 
single cell. 

The internal resistance of a battery in parallel is the 
resistance of one of the cells divided by the nujnber of cells. 




212 ELECTRICITY [§§ 355-356 

The E.M.F. of a battery in multiple series is the U.M.F. 
of one of the sets or series. 

The internal resistance of a battery in multiple series is 
the resistance of one of the sets or series divided by the 
number of sets. 

356. Best Arrangement of Cells. — In a general way it 
may be said that the best arrangement of cells is the one 
which will make the internal resistance as near the exter- 
nal as possible. The flow, or strength, of current, deter- 
mines, usually, its value ; and the following formulas will 
give the flow in amperes, with the connections indicated. 

WW IP 

Series: 0= ,/ , ^ (1). Parallel: C = —^^— (2). 
Nr -\- It ^,T> 

Multiple series : O = -^ (3). 

In these formulas, N is the number of cells in a set, P 
the number of sets in parallel, r the internal resistance of 
a single cell, E the E.M.F. of one of the cells, and R the 
resistance of the external circuit. 

Now let us see by which arrangement we get the greatest 
current. 

Suppose we have 6 cells connected in series, each cell 
having an E.M.F. of 2 volts and an internal resistance of 
1.5 ohms. What flow will they give through an external 

resistance of 7 ohms? 

6x2 
Substituting in (1), we have = - -—^ — ^=-75 

amperes. 

The same cells connected in parallel will give what flow 

through the same external resistance ? 

2 
Substituting in (2), we have C = j-= = .27 + . 



§356] ELECT BIC CUE RENTS 213 

-With the same cells connected in two sets of three each, 

what flow will be given ? 

3x2 
Substituting in (3), we have = -^ =— p =.65-. 

2 

In the first case the current is strongest, and the inter- 
nal resistance is nearest the external. 

Again, find the best arrangement of eight of the above 
cells it R is 4: ohms. 

In this problem we need only find the arrangement 
which will give us an internal resistance nearest the 
external. If Ave connect the cells in series the internal 
resistance will be eight times 1.5, or 12 ohms, which is 
much more than the external resistance. If we connect 
them in two sets of 4 cells each, the internal resistance 
will be four times 1.5 divided by 2, or 3 ohms. It is at 
once evident that the second arrangement gives an inter- 
nal resistance nearer the external, when the external 
resistance is 4 ohms. But when the external resistance 
is 10 ohms, say, the first arrangement will make the resist- 
ances more nearly equal. By applying the formulas, the 
flow in each case may be determined, and the statements 
proved. 

EXERCISES 

1. Find the resistance of 500 ft. of copper wire which is 
5 mils in diameter. 

2. Find the resistance of 1 mi. of No. 16 iron wire. (See 
page 374 for diameter of wire'.) 

3. Find the resistance of 2000 ft. of German-silver wire 
1.5 mm. in diameter. 

4. Ten cells in series, each having a voltage of 1.5 and an 
internal resistance of 1 ohm, will give what flow through an 
external resistance of 30 ohms ? 



214 ELECTRICITY [§ 857 

5. Twenty gravity cells connected in series, each having a 
voltage of 1 and an internal resistance of 2 ohms, will give 
what flow through 2 mi. of No. 18 iron wire ? 

6. What will be the best arrangement of 10 of the cells 
given in problem 5, if the external circuit has a resistance of 
5 ohms ? 

7. What will be the best arrangement of the cells if the 
external circuit consists of 1000 ft. of No. 20 copper wire ? 

8. If wire 32 mils in diameter and 2000 ft. long has a 
resistance of 36.5 ohms, what is its resistance constant ? 

9. Given 16 cells, each having a voltage of 1.8 and an 
internal resistance of 1.4 ohms ; find the arrangement which 
will give the maximum flow through an external resistance of 
4 ohms. Show the arrangement by a diagram. 

10. What must be the size of iron wire to have the same 
resistance as an equal length of No. 20 copper wire ? 

11. 2000 ft. of copper ware has a resistance of 1.18 ohms. 
Find its diameter. 

12. A coil of aluminum wire 20 mils in diameter has a 
resistance of 50 ohms. Mnd its length. 

13. If 1000 ft. of wire, having a diameter of 30 mils, has a 
resistance of 35 ohms, what is its constant ? 

14. Find the best arrangement of 12 cells, each having a 
voltage of 2 and an internal resistance of .6, if the resistance 
of the external circuit is 5. 



SECTION 5. EFFECTS OF ELECTRIC CURRENT 

357. Heat Effects of a Current. — When a large flow of 
current passes through a small conductor, the conductor 
becomes hot, and may melt unless care is exercised. It 
is found that the amount of heat produced is propor- 
tional to the resistance. An increase of flow increases 
the amount of heat produced ; and, of course, the amount 
of heat is proportional to the time. Experiment shows, 
however, that if we double the floiv through a certain 



§§ 357-358] EFFECTS OF ELECTRIC CURRENT 215 

resistance, the heat evolved is four times as great as 
before, and if the current is trebled, the heat effect is 
increased ninefold. From the above facts we deduce the 
following law, which is known as Joule's Law : 

The heat developed in a conductor is directly proportional 
to the resistarice of the conductor^ to the time of flow ^ and to 
the square of the strength of the current. 

If the entire energy of the current is converted into 
heat, the number of calories of heat may be determined 
by the following formula, in which t represents the time 
the current flows : 

Heat, in calories, iH)= C^Etx 0.24. 

358. Chemical Effects of a Current. Electrolysis of 
Water. — If the terminals of a strong cell or battery are 
placed in a dish of water in which has been placed a little 
acid, bubbles will rise to the surface from each electrode. 
If a piece of apparatus arranged as in Fig. Ill is used, in 
which the electrodes are pieces of platinum foil or wire 
embedded in wax or fused through the 
glass, the liberated gases may be collected 
in tubes as shown, the water being dis- 
placed as the gas passes in. It will be 
found that the gas will collect twice as 
fast in the tube over the — electrode as . 
in the one over the + electrode ; and a test will show 
that the gas collecting the more rapidly is hydrogen, 
and that the other is oxygen. As the current passes 
through the water a change takes place, which we call ion- 
ization; the molecules are dissociated into ions. In this 
case the ions are composed of oxygen and hydrogen. 
The oxygen which goes to the + electrode, or anode, is 
called the anion, while the hydrogen which collects at the 
— electrode, or cathode, is called the cation. Many other 
compounds, such as copper sulphate and silver nitrate in 




216 ELECTRICITY [§§ 358-360 

solution, become ionized upon the passage through them 
of a current of electricity. 

359. Electroplating. — If a piece of carbon is fastened to 
the wire connecting it with the negative electrode of a 
battery, and a piece of copper is attached to the positive 
electrode in the same Avay, and the two are placed in a 
strong solution of copper sulphate, it will be found that, 
as the current flows, copper is deposited upon the surface 
of the carbon. In this case the copper sulphate seems to 
be, broken up into copper and the ion SO^, the copper 
being the cation and the SO^ the anion. The copper is 
deposited upon the carbon cathode, and the SO^ takes hy- 
drogen from the water and forms sulphuric acid, H2SO4, 
which, in turn, attacks the copper, dissolving it, and form- 
ing more copper sulphate. 

This process is called electroplating, and it is, essen- 
tially, the method used in all silver- and nickel-plating. 
The object to be plated must be thoroughly cleaned, and 
the solution used is usually a cyanide of the metal with 
which the object is to be plated. 

360. Electrotyping. — When a large number of copies of 
a publication are to be printed, the type metal is found 
to be too soft for the wear ; so the process of electro- 
typing is often resorted to. The type for a page is set 
up, and an impression of it is made upon wax. This im- 
pression is carefully dusted with powdered graphite, Avhich 
renders the surface electrically conductive. The wax 
impression is then placed in a copper-2)lating bath and 
connected with the negative pole of a battery, in the same 
manner as any object to be plated, and a current is allowed 
to flow until a coating of copper, as thick as a sheet of 
heavy note-paper, is deposited all over the surface of the 
carbon. This coating conforms exactly to the surface of 
the wax, and thus duplicates the page of type. This sheet 



§§360-361] EFFECTS OF ELECTRIC CURRENT 



217 



of copper is backed up with melted type metal, and built 
up to the proper thickness to be placed in the printing- 
press. It will then wear to print many more copies of 
the page than the type would. 

361. Storage Cells, or Secondary Batteries. — If two 
plates of lead placed in a 20^o solution of sulphuric 
acid, are attached to the poles of a battery, and a cur- 
rent is turned on, the oxygen, which would be liberated 
at a platinum positive electrode, acts upon the lead and 
forms a coating of lead oxide. If both plates are covered 
with the lead oxide at the beginning of the process, the 
lead oxide upon the negative electrode is reduced; i.e.^ 
the hydrogen, liberated by the current, unites with the 
oxygen of the lead oxide and forms water, while the oxygen 
liberated at the other electrode forms more of the lead 
oxide upon the surface of that plate. After this process 
has gone on for a time, the plates are left in different 
conditions ; and if the battery is removed, and the wires 
attached to the lead plates are connected, a current of 
electricity will flow through the conductor in a direction 
opposite from that in which the current flowed during 
the process of charging. And while this current is flow- 
ing, the oxidized plate is being reduced and the other plate 
is being oxidized. This process will go on until the plates 
are in practically the same condition. Such an apparatus 
is called a storage, or secondary, cell. 

The commercial storage battery is 
made up of a series of lead plates, 
roughened and covered with a coating 
of lead oxide in the form of a paste. 
Alternate plates are connected in a set, 
as shown in Fig. 112, the plates being 
separated by some insulating material which will not be 
acted upon by the acid. The large number of plates thus 




Fig. 112. 



218 ELECTRICITY [§§ 361-363 

arranged gives a large surface for oxidation, and also 
makes the internal resistance very small. When a cell is 
charged from an outside source it will remain charged 
indefinitely in open circuit, and when the circuit is closed 
it will furnish almost as much energy as has been expended 
in charging it. ' 

362. Use of Storage Batteries. — Storage cells, or bat- 
teries, may be used for almost any purpose for which 
voltaic cells may be used. The difference between them 
is that the voltage of storage cells is usually higher — 
it is about two volts ; they are heavier, because of the lead 
plates required ; they require charging more frequently 
than voltaic cells require attention j and the current is, 
proportionately, considerably cheaper, being not much 
greater than that of the charging current generated by a 
dynamo. 

In general, storage batteries are ordinarily used where 
a heavy current is required, and a charging current is 
convenient. Among other purposes, they are used to run 
yachts and automobiles ; but for these purposes their use 
has been somewhat disappointing, largely because of the 
enormous weight required for a good working current ; 
they are, however, being developed to a high degree of 
perfection, and it is hoped will soon be quite practicable 
for these and other similar purposes. 

363. The Galvanoscope. — The fact that a current of 
electricity brought near a magnetic needle would cause it 
to deflect, as stated in Art. 332, was discovered by Oersted 
in 1819 ; and the principle has been applied to the con- 
struction of the galvanoscope and galvanometer. 

If an insulated wire, carrying a current, is placed 
parallel to the needle of a compass, a small deflection is 
observed. If the wire is carried once around the com- 
pass, the deflection will be nearly doubled, and if many 



§§ 363-364] EFFECTS OF ELECTRIC CURRENT 



219 




Fig. 113. 



turns surround the compass, by some such an arrange- 
ment as is shown in Fig. 113, a great deflection may be 
obtained from a very small current. 
Such an instrument, used simply to dis- 
cover the presence and direction of a 
current, is called a galvanoscope. If, 
however, the instrument is provided with 
a pointer and scale, so that the deflection 
can be accurately measured, w^e have a galvanometer. 

364. The Tangent Galvanometer. — The effect which an 
electric current has on certain apparatas gives a method 
by which the current may be measured. The tangent 
galvanometer (Fig. 114) is such an apparatus, used for 
measuring the electromotive force or the strength of cur- 
rents. It usually consists of a circular hoop, which may 

be a single large conductor or 
several turns of wire wound 
upon a wooden support, the 
ends of the wire being at- 
tached to binding-posts for 
the attachment of the con- 
ductors which connect the 
galvanometer with the source 
of current. In the center is 
suspended a short magnetic 
needle, which swings in a 
horizontal plane. Under the 
needle is placed a circular 
scale, graduated in degrees ; and at right angles to the 
needle is fastened a long, light pointer to facilitate the 
reading of the deflection. 

This instrument is called a tangent galvanometer^ 
because the strength of the current is directly propor- 
tional to the tangent of the angle of deflection which it 




Fig. 114. 



220 



ELECTRICITY 



[§§ 364-366 



causes. (See table of natural tangents, page 373.) So if 
we find the angle of deflection for a certain flow, say one 
ampere, we may determine the strength of any other 
current which is passed through the instrument by com- 
paring the tangent of its angle of deflection with that of 
one ampere. For instance, Q : Q' = tan. a : tan. a\ in 
which C represents the known current and Q' the unknown, 
and a and a' their respective angles of deflection. A 
certain factor, called the reduction factor, may be deter- 
mined for each galvanometer. This factor is a value such 
that the tangent of the angle of deflection being multiplied 
by it will give the flow in amperes. 

365. The Astatic Galvanometer. — The astatic galvan- 
ometer, shown in diagram in Fig. 115, consists of a long 

coil of insulated wire wound in two sec- 
tions, and a double needle, the two needles 
being of nearly equal strength and fast- 
ened together as shown, with like poles 
in opposite direction, so that the whole 
is nearly independent of the magnetic 
effect of the earth or of neighboring magnets. Two 
needles seldom have exactly equal 
strength ; so the combination has 
a very slight tendency to stand 
in a north and south direction ; 
but it is much more readily de- 
flected than a single needle, and 
thus will show the presence of a 
much weaker current. Figure 116 
shows one of the common com- 
mercial forms. 

366. The D'Arsonval Galvan- 
ometer. — Another form of galvanometer, which is now 
largely used for very delicate work, is the D'Arsonval, 



Fig. 115. 




Fig. IIG. 




§ 366] EFFECTS OF ELECTRIC CURRENT 221 

which is a horseshoe magnet with a coil of wire suspended 
between the poles. The force which holds the coil in 
position is the torsion of the suspending wire, and this 
can be made as small as desired. The gen- 
eral arrangement is shown in Fig. 117. 
The instant that a current flows through 
the coil, it produces magnetic effects 
which tend to make the coil turn at right 
angles to the plane of the horseshoe 
magnet. A mirror attached to the coil, 
by reflecting a beam of light, allows slight 
deflections of the coil to be noticeable. 
One of the great advantages of this form of galvanometer 
is that it is "dead beat," that is, it will come to rest very 
quickly without much vibration, vibrations causing much 
waste of time in the use of the other forms. Another 
advantage is that it is not affected by external magnetic 
effects. There are many modifications of this type of 
instrument, but all work on the same principle. 

For commercial purposes, voltmeters are ordinarily used 
for measuring electromotive forces, and ammeters for meas- 
uring strength of currents. These are considered in the 
next section. 

EXERCISES 

1. If a flow of 1 ampere deflects the needle of a tangent 
galvanometer 12°, what will be the strength of a current which 
will cause a deflection of 30° ? 

2. The reduction factor of a tangent galvanometer is 3. 
What is the current when the deflection is 30° ? 

3. A flow of 1.5 amperes through a tangent galvanometer 
produces a deflection of 23°. Another source of current 
causes a deflection of 35°. Find the strength of the second 
current. Find the reduction factor. 



222 ELECTRICITY [§ 367 

4. How may a storage battery of 12 cells, of 2 volts each, be 
connected to give 4 volts ? 3 volts ? 

5. A current of electricity is passed through a bath of copper 
sulphate between copper electrodes for 10 minutes, and it is 
found that the — electrode has gained .5922 g. in weight. Find 
the current strength. 



SECTION 6. ELECTRICAL MEASUREMENTS 

367. Fall of Potential. — We find that, as a current flows 
through a conductor, the resistance of the conductor causes 
a fall of pressure or potential, just as water flowing through 
a long small pipe loses more or less of its pressure. It is a 
well-known fact that, where there is an extensive water- 
works plant with one central station, the pressure is not so 
great at a long distance from the head as it is nearer ; that 
the farther one goes from the head the less is the pressure. 
And it is evident that, if the pipes were extended away 
far enough, a point would be reached where the pressure 
would not be sufficient to force the water through the 
pipes — the pressure would be all used up. 

It is very similar with electric pressure. Replace the 
pipe by the external circuit, say, of wire ; as we go farther 
from the positive pole of the battery or dynamo, the press- 
ure becomes less and less, until, finally, when the circuit 
is completed, the pressure is all used up. In case of the 
water, the force, which we call pressure, is exhausted in 
forcing water through the pipe ; in case of the electric 
current, the force, which we call electromotive force, is 
used up in forcing the current through the wire. There 
is, however, this difference : No matter how short the wire, 
or how slight its resistance, the electromotive force is used 
up in pressing the current through. If the resistance is 
slight enough, and the electromotive force high enough, 



§§ 367-368] ELECTRICAL MEASUREMENTS 223 

the energy uses itself up in heating and even melting the 
wire. 

As a necessary consequence of this, the pressure, or po- 
tential as it is called, not only diminishes, or falls, in going 
from the beginning to the end of the circuit, but, the 
fall is exactly proportional to the resistance passed through. 
When the resistance has been half overcome the potential 
is also one-half. If the total resistance is 12 ohms and the 
electromotive force of the battery or dynamo is 24 volts, 
there will be a fall of 2 volts in every ohm passed through ; 
when the current has been pushed through 2 ohms the 
potential is 20 ; when through 8 ohms, it is 8 volts, as two- 
thirds of the resistance is overcome and hence two-thirds 
of the force is used. 

And in this connection it should be remembered that if 
two points of different potential are connected by a con- 
ductor, there will be a flow of current from the point of 
high to the point of low potential. 

The student, however, must not be misled by the expres- 
sions used here, and especially by the water analogy. The 
electric current is nothing tangible, such as water or gas ; 
there is no flow such as we have with fluids. Perhaps all 
we can say of it is that there is a passage of energy along 
the wire due to some effect in the ether which selects the 
wire as the easiest, passageway. In fact the passage seems 
to be more through the ether than through the wire, and 
no more in one direction than in the other ; but as a matter 
of convenience passage in the wire, and in a certain direc- 
tion, is assumed. 

368. Effect of Resistance on Current. — The effect of the 
resistance on the current is very different from its effect 
on the pressure. It is immaterial how long a pipe may be, 
or how much the pressure may be reduced in pushing the 
water through ; it is evident that no more water will flow 



224 



ELECTRICITY 



[§§ 368-369 




Fig. 118. 



through any portion of the pipe than flows out at the end, 
provided there are no intermediate inlets or outlets. Nor 
does it matter how large or small certain portions of the 
pipe may be, nor whether some portions run upward and 
others downward ; the flow through any portion will 
necessarily be the same as through any other portion. 

It is just the same with the electric current; no more 
current can flow through one portion of the circuit than 

flows through any other 
portion, provided it is 
a continuous circuit, 
without inlets or outlets. 
Thus we may have a 
motor in series with a 
lot of lamps as indicated in Fig. 118 ; the resistance of 
the lamps may be a thousand times that of the motor, 
but the current through them will be the same as through 
the motor. Yet, in accordance with the last Article, the 
fall in potential will be a thousand times as much through 
the lamps. 

369. Shunt or Divided Circuits. — Sometimes it is con- 
venient to provide two or more paths for a current, as 
shown in Figs. 119 and 120. In such a case 
the current divides, and a part follows each 
arm or branch of the circuit. According to 
Ohm's Law, the current flowing through a 
conductor is inversely pro- 
portional to the resistance. 
In Fig. 119, if the arm x 
has twice as much resistance as the arm 
?/, y will carry twice the current that is 
carried by x. If, as in Fig. 120, we have 
several conductors of equal resistance, each will carry an 
equal amount of current ; and, if the voltage remains con- 




FiG. 119. 




Fig. 120. 



§369] ELECTRICAL MEASUREMENTS 225 

stant, the four will carry four times as much current as 
one. Hence, according to Ohm's Law, the resistance of 
the part of the circuit formed by the conductors 6, /, g^ 

and h will be one-fourth that , 

of any one alone, just as four ^ ^ 

small pipes connecting two 
mains, as indicated in Fig. 121, 
will carry a barrel of w^ater in ^ 



one-fourth the time that one of ^^' " ' 

them will. In these figures, the conductors are connected 
in parallel ; and this method of connecting, as with the 
cells of a battery, divides the resistance. 

The following formula represents the combined resistance 
of conductors connected in shunt : 

R r r'' 

in which R is the combined resistance, and r and / are the 
resistances of the arms of the circuit. Placing two con- 
ductors parallel is the same as making one of them twice 
as large, and thus reducing its resistance one-half and 
douhling its conductivity. Thus we say that the resist- 
ance of a conductor is the reciprocal of its conductivity. 
The conductivity of the conductors, we can readily see, is 
the sum of their conductivities ; and so, of course, the 
reciprocal of their combined resistance equals the sum of 
the reciprocals of their respective resistances. Simplify- 
ing the abov^ equation we have : 

...J 
R 



r -\- r' 



Hence the combined resistance of two arms of a shunt circuit is 
the product, divided hy the sum, of their respective resistances. 
If there are three or more conductors connected in parallel, 

Q 



226 ELECTRICITY [§§ 369-370 

where the divisions have different resistances, the formula 
must be applied to two at a time. If there are three con- 
ductors, find, by means of the formula, the resistance of a 
pair of them, and then apply the formula to the result 
obtained and the remaining resistance. If there are four 
conductors, find the resistance of the two pairs and then 
apply the formula to these results. 

370. Effect of Shunts. — For reasons that will be appar- 
ent later, the effect of shunts on potential and current is 
very important. When we have a circuit as indicated in 
Fig. 119, consisting of a single wire in series with a set of 
two in parallel, we may consider the shunt wires by them- 
selves first, and then in connection with the single wire. 

Suppose a and h to be the poles of the battery ; it will 
push the current through both x and ?/, just as the water, 
as indicated in Fig. 122, would be forced through u and v. 

The potential at the end of x 
would be the same as at the end 
of y, just as the pressure at the 
end of u would be the same as 
^^' "■ at the end of v^ no matter what 

the respective resistances may be. And it is immaterial 
how many branches there are. Hence in shunt wires, or 
any resistances in parallel, the fall of potential between 
the points of connection is the same in all branches. 

If, now, we consider the current^ it seems clear that the 
flow through the respective wires will be inversely propor- 
tional to the resistances, just as it would be with the flow 
of water through u and v. The pressure at the beginning 
and at the end is the same ; and if the resistance of one 
wire or pipe is ten times that of the other, necessarily it 
will pass only one-tenth as much current. Or, according 
to Ohm's Law, electromotive force being the same, current 
is inversely proportional to the resistance. 




§§370-372] ELECTRICAL MEASUREMENTS 227 

Suppose, now, the poles to be a and c (Fig. 119). 
Considering x and y as a single resistance, the fall in 
potential in it would be to the total potential as its resist- 
ance is to the total resistance. With two wires the only 
difference is, the resistance of the two would be less ; the 
fall would still be proportional to their resistance ; and it 
would still necessarily be the same in each. 

Evidently with c as the negative pole, the currents 
flowing from x and y would both flow into c, and the only 
effect would be to reduce the current flowing, as the resist- 
ance would be increased. The currents through x and y 
would still be inversely proportional to their resistances, 
and that through be would equal the sum of those through 
X and ?/. This may be made clearer with the water-pipes, 
if it is confusing. 

371. Summary. — The foregoing three articles may be 
gathered together in the following summary : 

The potential of the circuit aliv ays falls to zero. 

The fall in potential is proportional to the resistance passed 
through. 

There is ahuays a current along a conductor from a point 
of high to a point of low potential. 

The current is the same at all points of a simple circuit. 

With shunts., the fall in potential between the points of 
connection is the same through all branches. 

The currents in the branches are respectively inversely pro- 
portional to the resistances. 

Tlie current before and after the connecting points equals 
the sum of the currents through the branches. 

372. Measurement of Potential. — The electromotive 
force of a circuit is the total pressure between the two 
poles of a battery ; the potential is the pressure or differ- 
ence in potential between any two intermediate points. 
If it is desired to measure the electromotive force, the 



228 



ELECTRICITY 



[§§ 372-373 




poles of the galvanometer or voltmeter are connected 
directly with the poles of the battery or dynamo, as indi- 
cated in Fig. 123, G- being the galvanometer and B the 
battery ; the voltmeter becomes then a shunt 
to the main circuit, and the fall in potential 
through it is the same as that through the 
main circuit, and equals the entire potential, 
or the electromotive force. If it is desired to 
measure the fall of potential through some portion of a cir- 
cuit, through a lamp, sa}", the poles of the voltmeter are 
connected respectively with the wires leading in and out 
of the lamp, thus forming a shunt with the lamp. 

As the currents flowing through shunts are inversely 
as the resistances, the resistances of voltmeters or galvan- 
ometers are usually made very high, 
so as to reduce as much as possible 
the current flowing through them, 
and thus avoid robbing the other 
branch. High resistance also in- 
creases the sensitiveness in many 
cases. The resistance is frequently 
as high as 5000 ohms. A common 
form of voltmeter for stationary use 
is shown in Fig. 124. 

373. Measurement of Current. — The instrument ordi- 
narily used for measuring the strength of the current is 
called the ammeter, a common form 
of which for portable use is shown in 
Fig. 125. Voltmeters and ammeters 
are very similar in appearance, station- 
ary ammeters frequently being similar 
to Fig. 124 and portable voltmeters 
similar to Fig. 125. 
As the current through the circuit is the same at all 




Fig. 124. 




Fig. 125. 



§§373-^74] ELECTRICAL MEASUREMENTS 229 

places, evidently, in measuring the current, it is immaterial 
where the measurement is taken. On the other hand, as 
the flow through shunts depends on the resistance, the 
ammeter should not be connected as a shunt, as this would 
measure simply the current flowing through the ammeter 
and not at all the current sought. So the ammeter, while 
it may be connected on at any point, must always be con- 
nected in series. 

As the current through a circuit is inversely proportional 
to the resistance, it is evident that the resistance of the 
ammeter should be as low as possible, as otherwise the 
instrument itself would diminish too greatly that which it 
is intended to measure. If it is desired to be very accurate, 
the resistance of the ammeter with respect to the entire 
resistance should be known, and the reduction in current 
due to the ammeter considered. 

374. Resistance-box. — In order to measure the resist- 
ance of any conductor of electricity, a resistance box is 
usually used. Figure 126 shows the general plan of such a 
box. p and p' are the poles of the ^ 

box which receive and pass along the 
current ; tu^ x^ y, and z are blocks of 
brass or copper ; m, n^ and o are plugs, 
which, when inserted as shown, con- 
nect the blocks so the current can pass 

. -,, . Fig. 126. 

along with practically no resistance 

from p to p' \ a, 6, and c are coils of wire having various 

resistances. 

When the plugs are all in, the resistance of the box is 
practically zero ; but when a plug is pulled out, the current, 
in order to pass, must go through the coil connecting the 
blocks. So the resistance may be varied by pulling out 
different plugs. The boxes are frequently made with 
three sets of plugs, as shown in Fig. 127. The first set of 





230 ELECTRICITY [§§ 374-375 

plugs separate blocks which are connected by wires having 
resistances varying from . 1 ohm up to 1 ohm ; the second 
from 1 ohm up to 10, and the third from 10 up to 100. In 
this way the resistance may be varied 
by tenths of an ohm from .1 ohm up 
, , ^^^^.j-™^^™^ to several hundred ohms. 

I / The coils are usually wound double, 

so that the current goes around the 
coil and then right back along a 
parallel path. This is to prevent the 
formation of a magnetic field, the returning current 
neutralizing the magnetic effect of the first wire. The 
reason for this will be better understood after studying 
induced currents. 

375. Rheostat. — Resistance-boxes are frequently called 
rheostats. But, in practice, the tendency is to apply the 
term rheostat to a set of resistances, not necessarily coils, 
which are so arranged that the resistance may be varied 
by merely turning a lever. The primary purpose of the 
resistance-box is to control the resistance which the current 
passes through, while that of the rheostat is to control the 
current which passes through some other apparatus. 

The rheostat is used for many practical purposes, in 
fact, in nearly all cases where it is necessary to gradually 
increase or decrease the current flowing through any con- 
trivance. For permanently diminishing the current, its 
use is somewhat objectionable, as energy is wasted. When, 
as is frequently the case, the lamp of an optical lantern is 
run in series with a rheostat, and the resistance of the 
lamp is about equal to that of the rheostat, the energy used 
in the rheostat is about equal to that used in the lamp. 
In all such cases, the better way, where practicable, is to 
control the electromotive force of the current when gener- 
ated. 



§§ 376-377] 



ELECTRICAL MEASUEE2IENTS 



231 





^4^ 



Fig. 128. 



Fig. 129. 



376. Measurement of Resistance by Substitution. — To 

measure the resistance of any conductor by the process 
called substitution, the conductor is placed in series with a 

galvanometer, or voltmeter, as 

shown in Fig. 128, the current 

is turned on, and the reading 

of the galvanometer carefully 

taken. The conductor is then 

replaced by the resistance-box 

MB, as in Fig. 129, and plugs 
are removed until the galvanometer reads the same as 
before. The resistance indicated by the box will be the 
same as that of the conductor the resistance of which was 
sought. 

377. The Wheatstone Bridge. — One of the commonest 
and best methods of measuring resistance, and one which 
involves the principles stated in Art. 371, is by means of 
the Wheatstone bridge. As this is a difficult piece of 
apparatus to understand, and as its use is very important 
in the laboratory, it may be well to consider first the anal- 
ogy between it and water-pipes. 

Let Fig. 130 represent a set of water-pipes, with a 
stream of water at constant pressure flowing in from the 
vessel A. The pipes 
NO and PQ are con- 
nected by a pipe 
M which represents 
the "bridge." The 
stream of Avater 
Avill divide and flow 
through both pipes, and if they are of the same length and 
uniform in size throughout, there will be no tendency for 
it to flow through the bridge M, for will carry the same 
amount as iV, and Q the same as P. But if the valve a be 



^ 



Fig. 130 



^" ^^^ 



232 ELECTRICITY [§§377-378 

partly closed, it will increase the resistance to the flow 
through P, so P will carry less than the capacity of §, and 
there will be a flow from ^ to J" to supply Q. The only 
way to balance the flow, so there will be no flow through 
the bridge, will be to partly close the valve 6, so P and 
Q will have the same capacity, or to partly close N and 
decrease its capacity so that its capacity with respect to 
that of will equal the capacity of P with respect to Q ; 
or, so that N.O=P:Q. 

This is exactly analogous to the Wheatstone bridge; 
replace the horizontal tubes by electric conductors, the 
stop-cocks by electric resistances, the vessel A by an elec- 
tric generator, and insert a galvanometer in the " bridge " 
M^ so that a current through it may be detected, and the 
statement still holds good. When we have resistances 
N : =P : Q, current will not flow through the galva- 
nometer ; otherwise it will. 

Figure 131 represents a common form of the Wheatstone 
bridge. JL, B, (7, and D are squares of brass or copper 
strips, or bars, having a large cross-section, and hence low 

resistance. The arms AB, BC^ 
CI), and DA are broken at m^ n, 
0, p, as shown in the diagram. 
At m and 7i are coils of Avire, 
usually having equal resistances; 
at p is connected the resistance 
box BBj and at o is connected the 
conductor of wdiich the resistance 
is to be measured. The wires from the battery, or other 
source of current, are connected at B and D, as shown ; 
and a galvanometer is attached at A and C. ^ is a con- 
tact key for making and breaking the current. 

378. Measurement by Wheatstone Bridge. — Now sup- 
pose we make the connection as shown, and take out plugs 




§§378-379] ELECTRICAL MEASUREMENTS 233 

from the resistance-box until we are sure that the resist- 
ance of BB is greater than i^, and press the key. We 
shall find that we get a deflection of the galvanometer 
in one direction; then, if we make B greater than BB, 
the deflection will be in the opposite direction. We may 
be sure B is greater than BB if all the plugs are in 
the box. 

After the above discussion, it is not difficult to see why 
we have these deflections. If BB is greater than B, its 
capacity or conductivity will be less, and the fall in poten- 
tial through it will be greater than through B. At the 
same time, as the resistances m and 7i are equal, the fall 
will be the same through each. If this is so, the potential 
of the current at C will be higher than at A ; and, as these 
two points are connected by a conductor through the gal- 
vanometer, there will be a flow of current from C to A 
through G-. If we now put plugs into the resistance- 
box until BB is less than B, the potential will be higher 
at A than at O, and, consequently, there will be a cur- 
rent through Gr in the opposite direction. If we vary 
the resistance of BB^ until there is no deflection of (r, we 
know there is no difference of potential between A and (7, 
and that B and BB are equal ; because, to have no cur- 
rent, we must have BB : B = m : n, and jn equals n. 

379. The Slide-wire Bridge. — The slide-wire bridge is 
a modification of the Wheatstone bridge, used for the 
same purposes. In principle they are the same except that 
with the slide- wire bridge the resistances m and n (Fig. 131) 
are not usually equal, and may be readily changed in value 
by merely sliding a contact point along a wire of high 
resistance. One of the common forms of the bridge is 
shown in Fig. 132. A, B, C, B. E, F, a, H, and I are 
binding-posts for attaching wires, placed upon heavy bars 
of brass or copper, with practically no resistance ; AB is a 



234 



ELECTRICITY 



[§§ 379-380 




piece of high-resistance wire, usually German-silver or 
platinoid; J" is a piece of metal, carrying a binding-post, 
and grooved to slide u]3on a scale CT, which is graduated 

to millimeters. X, 
the end of J", stands 
above the wire AB^ 
so that contact with 
the wire may be 
made by pressing L 
down. RB is a 
resistance-box, and 
R is the resistance 
to be measured. The wires carrying the current from 
the cell are attached at C and /; and the current flowing 
in at I divides and floAvs in parallel through AB and the 
other branch, containing RB and R. 

380. Measurement with the Slide-wire Bridge. — In 
measuring with the slide-wire bridge the method em- 
ployed is very similar to that with the Wheatstone bridge. 
The resistance to be measured, R^ is connected to the bind- 
ing-posts D and E. Then, if L is exactly at the middle 
of the wire AB^ and R is equal to RB^ the arrangement 
will be just as the one discussed with the Wheatstone 
bridge, and no current will flow through Gr. But suppose 
that R is one-half as great as RB. Then according 
to the discussion, there will be a flow through (x, be- 
cause the fall through IL will equal that through LC^ 
while the fall through CF will be only one-half that 
through FI \ so L will have a higher potential than F^ 
and there will be a flow from L to F through Cr. In 
such case, in order to have no current through Gr, we 
must slide J toward B until the resistance of LC is one- 
half that of IL. Then the potential at L will equal that 
at F, there Avill be no current through Gr, and Ave have the 



§ 380] ELECTRICAL MEASUREMENTS 235 

proportion IF : FQ =IL : LC. And as the bars have no 
appreciable resistance, we have BB : B = AL : LB. 

Hence, in order to determine the value of B, we have 
only to slide J" along until the current through G- ceases, 
and measure the lengths, by comparing with the millimeter 
scale, of BL and LA, The resistances of B and BB will 
be proportional to these lengths. If LB is 550 mm. long, 
and LA is 450 mm. long, and BB indicates a resistance of 
30 ohms, we have the proportion 550 : 450 = i^ : 30, and 
B = 36|- ohms. 

EXERCISES 

1. If the poles of a battery are connected by means of two 
wires in parallel, one having a resistance of 6 ohms and the 
other of 8 ohms, what will be the combined resistance of the 
external circuit ? 

2. Two electric mains are connected by four conductors in 
parallel, having, respectively, resistances of 3, 5, 7, and 8 ohms ; 
find the combined resistance of the four. 

3. To the poles of a storage battery are connected in parallel 
a motor, having a resistance of 12 ohms, a resistance box, with 
a resistance of 15 ohms, and a plating bath having a resistance of 
5 ohms. Find the combined resistance of the external circuit. 

4. Four wires are connected in parallel ; the first consists of 
500 ft. of No. 18 iron wire, the second of 300 ft. of No. 20 plat- 
inum wire, the third of 400 ft. of No. 17 German-silver wire, 
and the fourth of 600 ft. of No. 16 iron wire. Find the com- 
bined resistance. 

5. A 110-volt current flows through two motors in series 
having resistances of 10 and 15 ohms respectively, (a) What 
is the fall of potential through the first motor ? (6) What is 
the flow of current through the first ? the second ? 

6. If the motors mentioned above are connected in parallel 
to the same circuit, what is the fall of potential through each ? 
what is the current through each ? through the dynamo ? 



236 ELECTRICITY 

7. A 220-volt current passes through four lamps in series, 
each having a resistance of 55 ohms. What is the flow through 
the lamps ? the fall of potential through each ? How many 
watts of power does the current represent ? 

8. A dynamo generates a current with an E.M.F. of 100 
volts. The current flows through a resistance of 10 ohms in 
series with a set of three resistances of 2, 4, and 6 ohms respec- 
tively in parallel. What is the total resistance of the circuit ? 

9. In Exercise 8 (a) what is the current through the 10 
ohms ? through each of the others ? (h) What is the fall of 
potential through the 10 ohms? through each of the other 
resistances ? 

10. A circuit consists of 20 ft. of No. 30 copper wire con- 
nected in series with a set of two wires in multiple of No. 36 
copper wire, one 18 ft. long and the other 24. Find the resist- 
ance of the circuit. 

11. If the centers of the two wires in Exercise 10 are con- 
nected by means of 8 ft. of No. 30 copper wire running north 
and south, and a compass placed under this wire, will the com- 
pass needle be deflected? If the end of the cross wire, or 
bridge, is moved toward the end of one of the other wires, w^hat 
will be the result ? why ? 

12. In the system above suppose the current is flowing from 
east to west Avith the 18-ft. wire on the south side of the sys- 
tem. If the end of the cross wire is moved from the center 
3 ft. east on the south wire, will there be a current through it 
and in which direction ? Which way and how much must the 
other end be moved to stop this flow through the bridge wire ? 

13. Given 8 cells, each having a voltage of 2 and an internal 
resistance of 1.5 ohms, find the best arrangement of the cells 
that will give a flow of 1 ampere through an external resistance 
of 5 ohms. 

14. What is the best arrangement of 12 of these cells if the 
external resistance is 2.2 ohms ? What would be the voltage 
of the battery in such case ? the current strength ? the power 
in watts ? in horse-power ? 



§381] 



EL ECTR OMA GNETISM 



237 



SECTION 7. ELECTROMAGNETISM 




Fig. 133. 



7 



381. Magnetic Effects of a Current. — As we have already 
seen, a wire carrying a current placed over a magnetic 
needle causes the needle to deflect, and tends to make it 
stand at right angles to the direction of 
the current. If a coil of wire is attached 
to the plates of a voltaic cell, so arranged 
that the coil and plates float upon the 
liquid of the cell, as shown in Fig. 133, 
it will be found that the coil 
tends to float pointing in a 
north and south direction ; and if the pole of 
a permanent magnet be brought near, it will 
attract one end of the coil and repel the other. 
If a wire thrust through a piece of card- 
board, as shown in Fig. 134, carries a strong 
current, and iron filings are sprinkled upon 
the cardboard, the filings will arrange them- 
selves in concentric circles around the wire, thus showing 
a decided magnetic field. 

A coil of wire arranged as in Fig. 133 is called a solenoid; 
and it is found that any coil of wire carrying a current has 
decided magnetic effects ; the more turns of wire the more 
decided the effects. Two solenoids suspended to move 
freely near each other act exactly like 
two magnets. Figure 135 represents 
a piece of apparatus, consisting of a 
coil of several turns of insulated wire 
passed through a heavy piece of card- 
board, which shows the magnetic field 
around a conductor very well. Iron filings sprinkled upon 
the cardboard arrange themselves as shown. If a compass 
be placed anywhere in this field, the needle will stand 



Fig. 13i. 




238 



ELECTRICITY 



[§§ 381-383 




nearly parallel to the lines of force as mapped by the lines 
of iron filings. If placed in the coil, it will take a posi- 
tion nearly at right angles to the plane of the coil. 

382. Mutual Action of Currents. — Tivo currents flowing 
in the same direction attract each other; hut if in opposite 
directions they repel each other. Figure 136 shows a piece 

of apparatus which proves the first state- 
ment very neatly. It consists of a coil 
of small, springy wire, suspended from 
a support so that the lower end dips just 
below the surface of the mercury in a 
mercury cup. The cell is attached to 
the upper end and to the mercury cup. 
When the current is turned on, the coils 
of the Avire attract each other, and the 
lower end of the wire is lifted out of the mercury, and 
thus the circuit is broken ; the coils then cease to attract, 
and the end of the wire drops back into the mercury, 
making the circuit again. This is constantly repeated, 
so that the wire springs up and down, alternately making 
and breaking the circuit. 

383. The Electromagnet. — If we wind insulated copper 
wire, several layers deep, around a cardboard tube, or 
hollow wooden spool, we find that, when carrying a cur- 
rent, the wire produces magnetic effects. 
And if we place a bar of soft iron in the 
coil, as shown in Fig. 137, we shall very 
greatly increase the magnetic effects. 
The iron seems to attract the lines of 
force, and this property is called the permeability of the 
iron. Different grades of iron vary greatly in perme- 
ability, which seems to increase with the purity and 
malleability of the iron. 

The strength of a magnet., the coil remaining the same., is 




Fig. 137. 



§§ 383-385] ELECTROMAGNETISM 239 

proportiojial to the strength of the current; or^ if the current 
strength remains the scime, the strength of the magnet is 
'proportional to the number of turns of ivire surroiincling the 
core or iron bar. 

Combining these statements, electricians say that tlie 
strength of an electromagnet is proportional to the num- 
ber of ampere-turns. That is, if one turn of wire carrying 
one ampere of current has a certain strength, or gives a 
certain magnetic effect, ten turns of wire carrying three 
amperes will be thirty times as strong. 

An electromagnet with a soft iron core retains its mag- 
netism only while the current is flowing, a fact which is of 
great importance commercially, as we shall see later. 

384. Poles of an Electromagnet. — An electromagnet has 
two poles, the same as any other magnet ; and, if the 
direction of the current around the core is known, we may 
distinguish between the poles of the magnet without test- 
ing with a magnetic needle. Suppose we have a bar 
magnet and know the direction of the current ; grasp the 
magnet in the right hand, the fingers pointing in the 
direction in which the current flows, and the thumb will 
point in the direction of the north pole of the magnet. 

Reversing the direction of the flow of current reverses 
the poles of an electromagnet. Reversing the winding of 
a coil, the current flowing through it from the same end 
all the time, reverses the poles of a magnet. 

One of the most important appli- 
cations of electromagnetism is 
in telegraphing, which we will 
now consider. 

385. The Simple Telegraph. — 
Figure 138 is a side view of a 
simple telegraph sounder; Fig. 139 
represents the front of the same "^ fig. 138. 




240 



ELECTRICITY 



[§385 



with D removed. M in each figure represents an electro- 
magnet with core projecting above the brass sounding 
bar ; / an iron crosspiece fastened at right 
angles to B ; P the point where B is 
pivoted to the support A; J) a piece of 
^ brass placed as shown; and and C 
screws for adjusting the stroke of B^ so 




Fig. 139. 




Fig. 140. 



that / cannot touch the 

core of M, nor get too 

far from it. If a current 

is passed through M by 

closing the contact key 

shown in Fig. 140, M 

will be magnetized, and 

/ will be attracted, causing C to strike I) with a sharp 

click. If the current is broken, M is demagnetized, and 

a spring S pulls B up to C. 

The Morse alphabet consists of various combinations of 
dots and dashes. A dot consists of a quick depression and 
release of the key which causes two clicks in quick suc- 
cession ; double the time between the clicks and we have 
the dash ; treble it and we have the double dash. Count 
one for the dot, two for the dash, and three for the double 
dash. The following is the complete Morse alphabet : 



A .- 


H . • . . 





U • 


B 


I . . 


P 


y . 


c . . . 


J 


Q 


w . 


D -. . 


K 


E 


. . . X . 


E . 


L — 


S 


Y . 


F . - . 


M -- 


T 


z . 


G --. 


N - . 







Figure 141 represents a simple telegraph system for two 
stations. The outfit at each station consists of a key K 





i 



§§ 385-386] ELECTROMAGNETISM 241 

and a sounder S. When the line is not in use the circuit 

is kept closed by means of a switch or lever L (Fig. 140). 

There is but one line wire used, the earth completing the 

circuit, as shown. The ground wires, as they are called, 

are soldered to metal plates, which are buried in the earth 

so deep that they are always in contact with moist earth. 

The current is furnished by a closed-circuit battery, usually 

a gravity battery, or 

by a dynamo, so when , ^ . 

the circuit is closed j^" 

the current is flowing 

all the time, and the 

magnets are magnet- J=Earth Earth 

- Till 1 Fig. 141. 

ized and hold the 

sounding bar B (Fig. 139) firmly down by attracting the 
iron armature I. If X wishes to telegraph y, he opens 
his switch and signals Y by giving IF's letter or number. 
He then closes his switch and waits for Y to answer 
his signal, which Y does after opening his own switch. 
Y then closes his switch, and X opens his and sends his 
message. When the simple telegraph is used and there 
are more than two stations on the line, all of the sounders 
on the line repeat the message. 

386. The Relay. — When telegraph lines are very long, 
the resistance becomes so great that it is a difficult matter to 

get strength of current to 
make the clicks loud enough 
to be easily heard, so the 
relay system is resorted to. 
The relay is simply an auto- 
matic key, as shown in Fig. 
142. Figure 143 represents 
a relay system for two stations. BB' are the line bat- 
teries, hh' the local batteries, and KK' the keys in the line. 




Fig. 142. 



242 



ELECTRICITY 



[§§ 386-388 



When K is closed and K' open, if Y presses his key, the 
relay R will become magnetized, attract JL, drawing it 
against the contact C, and thus complete the local circuit. 
This magnetizes xS', causing a click, which corresponds 
to the sound produced by the relay ; but, being a short 




Earth 



Fig. 143, 




circuit of small resistance, the current is strong and the 
sound is much louder. Thus it will be seen, as has 
been stated, that the relay is an automatic key, and that 
the current in the line needs only to be strong enough to 
attract A, thus completing the local circuit. 

387. The Duplex and Quadruplex. — Upon the large tele- 
graph lines systems are in use which allow the sending of 
one or two messages each way at the same time, thus 
doubling or quadrupling the capacity of 
the line. These systems of telegraphy, 
although in common use, are too com- 
plicated to explain here, but if the stu- 
dent desires, he can look them up in 
books of wider scope or in technical 
works upon telegraphy. 

388. The Electric Bell. — The electric 
bell (Fig. 144) consists of a horseshoe 
magnet M^ a gong (r, an armature A^ to 
which the hammer H is attached, and a 
contact screw (7, which is passed through 
a post P. The armature is attached to 
Fig. 144. a binding-post by means of a spring aS', 




§§388-389] INDUCED CURRENTS 243 

which holds it away from the poles of the magnet, the end 
of the spring being pressed against the end of the contact 
screw C. p and p' are binding-posts to which the wires 
from the battery are attached, ^is a contact key or push- 
button. When ^is pressed, the current flows through j9 
to P, through C to S^ through S to 0, then through the 
magnet, magnetizing the cores, and back to the cell. As 
the cores are magnetized, A is drawn forward, causing H 
to strike the gong, but at the same time breaking the circuit 
at C by pulling S away from it. As the circuit is broken 
the cores are demagnetized, and the spring is allowed to 
throw the hammer back. This completes the circuit by 
bringing the end of the spring again in contact with C. 
This is repeated in rapid succession as long ^ 

as the key is pressed. ^ i ^ y 

Electric bells are always connected in a 

parallel, when there are several in one 'I'l 

•^ T^. ^ ir • T 1 • Fig. 145. 

circuit, i^igure 145 is a diagram showing 

four bells connected to ring with one push button K. 



SECTION 8. INDUCED CURRENTS 

389. Electromagnetic Induction. — We have learned that 
a magnet is surrounded by a field composed of magnetic 
lines of force ; and that, if two opposite poles are placed 
near each other, lines of force pass from one directly to 
the other. It is also true that the number of lines of 
force emanating from a magnetic pole increases with its 
strength. 

In 1831 Michael Faraday discovered that if a conductor, 
forming a complete circuit, was caused to cut lines of force, 
a current of electricity was generated in the conductor. 

If the terminals of a hollow coil of wire are attached to 
a sensitive galvanometer, as shown in Fig. 146, and a bar 



2U 



ELECTIiWITV 



[§§ 389-890 




magnet is tlirust into the coil, it will cause a deflection of 
the galvanometer needle ; but if the magnet is allowed to 
remain in the coil, the needle comes 
back to rest at 0, showing that the 
magnet at rest has no effect. With- 
draw the magnet, and we again get 
a deflection, but in the opposite direction. 
Changing ends with the magnet re- 
verses the results first obtained. But 
it is only while the magnet is in motion 
that any current is produced in the coil. 
We may, then, make the following 
statement : Whenever there is a cha^ige 
in the number of lines of force cutting 
a closed circuity no matter what the cause, 
a current of electricity will be generated in the circuit. Cur- 
rents generated in this manner are called induced currents. 
390. Direction of Induced Currents. — If we thrust the 
south pole of a magnet into the coil, as indicated in Fig. 

146, the current generated traverses the coil in the direc- 
tion shown by the arrows. That is, if we look down on 
the coil, the current flows around it in the direction of the 
motion of the hands of a watch. When the magnet is with- 
drawn, the direction of the induced current is reversed. 
Reversing the poles of the magnet 
reverses this order of things. Such 
a coil is called a secondary coil. 

Now, if we substitute a small electro- 
magnet for the bar magnet, as in Fig. 

147, and make and break the circuit in 
the inner, or primary, coil, we get the 
same results as when we thrust in and 




Fig. 147. 



withdraw the magnet. 

the same effect as thrusting in the magnet 



Making the primary circuit has 
and breaking. 



§§392-393] INDUCED CURRENTS 247 

An induction coil with a condenser, as shown in Fig. 
148, is usually called a Ruhmkorff coil. 

As has been said, the induced current is stronger at 
the break ; and at the break only, is the current strong 
enough to jump the gap between Tand T' . The difference 
between the strength of the induced current, at the make 
and at the break of the primary, is due to the fact that at 
the make the induced current is in the direction oi^j^osite to 
that of the primary, and thus the inductive effect of the 
primary, and the self -inductive effect of the secondary, are 
in opposite directions ; but at the break they are in the same 
direction, and the result is the stronger induced current. 

The electromotive force of the induced current depends 
upon the electromotive force of the primary and the ratio 
between the number of turns of wire in the secondary and 
in the primary coils. Suppose the secondary is made up 
of 10,000 turns of wire, and the primary of 100 turns ; 
the E.jM.F. of the secondary will be to the primary in 
the ratio of 10,000 : 100, or 100 times as high. But what 
is gained in voltage is lost in flow. So, if we have a flow 
of 10 amperes in the primary, the flow in the secondary 
will be but .1 of an ampere. Thus C x E \w each case 
is the same. But C x E equals the watts, or the rate at 
which the energy is being used. So this is as it should 
be ; there is no loss of energy in the transformation, which 
is according to the law of the conservation of energy. 

393. The Condenser. — The condenser L, Fig. 148, is an 
arrangement to prevent the j)assage of a spark at A when 
tlie current is broken. It consists of several sheets of tin- 
foil separated from each other by means of some insulating 
material such as shellacked paper or thin sheets of mica. 
Alternate sheets of foil are connected as shown in the 
diagram, and one set is connected to each wire that leads 
from the battery. These sheets of foil collect the extra 



248 ELECTRICITY [§§ 393-396 

current which would make a spark at A^ and otherwise 
materially increase the effectiveness of the coil. 

394. Uses of the Ruhmkorff Coil. — The Ruhmkorff coil 
is used to produce a current of very high potential. It is 
said that the difference of potential between two surfaces 
to cause the passage of a spark through 1 cm. of dry air is 
about 30,000 volts ; so it may readily be seen that a very 
high potential is obtained with machines and coils which 
give a spark 5 or 10 cm. in length, and sparks many times 
these lengths are often produced. 

Both the induction coil and the static machine are used 
with Geissler and Crookes tubes. 

395. Geissler Tubes. — Geissler tubes are glass tubes, 
filled Avith different gases reduced to a very low pressure, 
and sealed. Through the ends of the tubes are fused 

short pieces of platinum wire 
which are to be attached to the 
terminals of an induction coil 
or the poles of a static machine. 
When the current is turned on 
and sparks pass through the gas, 
the tubes become brilliantly 
lighted with colors which vary 
with the gas. This is caused by 
the discharge through the tubes 
being a quiet, convective dis- 
charge, the supposition being 
that the molecules of gas are attracted to the nearest 
platinum wire, where they become charged, and then 
are repelled toward the other end, where they exchange 
their charge for an opposite one, and are again repelled. 
Figure 149 shows some of the forms of Geissler tubes. 

396. Crookes Tubes. — An exhaustive study of the dis- 
charge of electricity through a nearly perfect vacuum has 




§§390-391] INDUCED CURRENTS 245 

the same as withdrawing it. When the primary circuit 
is made^ the induced current flows around the secondary 
in the direction opposite to that of the primary ; but at the 
hreak^ the two are in the same direction. In general, we 
may say that the induced current always opposes the 
action of the inducing element. In thrusting in a magnet 
the induced secondary current tends to oppose the entrance 
of the magnet ; and when the primary current is made, 
the secondary tends to oppose its flow ; but when the 
primary current is broken and the currents are both in 
the same direction their inductive effects combine in a 
way that will be explained later, with the result that the 
resultant current is stronger then than in the other case. 
391- Self-induction. — When a current is flowing through 
a straight conductor, and the circuit is broken, a spark 
will pass between the points of contact, which will vary 
with the E.M.F. of the current. If, however, we place 
an electromagnet, having the same resistance as the 
straight conductor, in its place, and again break the 
circuit, we will get a much larger spark. This is caused 
by self-induction. As there is a field of lines of force 
surrounding every wire carrying a current, it is evident 
that in a close coil, or helix, the lines surrounding each 
turn of wire must cut the surrounding coils ; and, as 
any change in the number of lines of force cutting a 
coil causes an induced current, it is evident that there 
will be an inductive effect in such a coil, both at the make 
and at the break of the circuit. The fact is that, when a 
circuit is made in a helix^ the self-induction hinders the flow 
of current through the coil ; and at the breaks the withdrawal 
of the lines of force tends to assist the flow of current. 
Because of the latter fact, the spark which passes when 
the circuit is broken is longer with a coil than with a 
straight conductor. 



246 



ELECTRICITY 



[§392 



JT. 



392. The Induction Coil. — But the most efficient ap- 
paratus for causing electric sparks, or discharges through 
air or gases, is the induction coil. This consists of a 
primary coil, of comparatively few turns of coarse 
wire, wound around a core made of a bundle of soft 
iron wires. The bundle is used because a solid core, 
when rapidly magnetized and demagnetized, becomes hot, 
and, further, does not become demagnetized as readily as 
the bundle of wires. The primary is surrounded by a 
secondary coil, consisting, usually, of many turns of fine 
wire. A current is sent through the primary coil, and it 
is interrupted b}^ means of a contrivance somewhat like 
the armature of an electric bell. Figure 147 shows in 
diagram the winding and arrangements of the parts of the 
coil. Figure 148 is a diagram of a longitudinal section of 
the same, with the addition of a 
conde7iser L. In each case C repre- 
sents the core, P the primary coil, 
aS' the secondary, V the vibrating 
spring, I a piece of soft iron attached 
to the end of F^ which is attracted 
by and draws V away from the 
contact screw B at the point A. 
T and T' are the terminals of the 
secondary coil. 
When the current is turned on to the primary, it passes 
as indicated by the arrows, and C is magnetized, attract- 
ing I and breaking the circuit at ^. At the break a 
current is induced in the secondary, which will jump the 
gap between T and T\ if this is not too large. As the cur- 
rent is broken at J., the core is demagnetized, and the 
vibrator flies back to B again, completing the circuit ; 
and this action continues rapidly, so long as the current 
flows to the primary. 



^==^ 




Fig. 148. 



§§ 397-398] 



INDUCED CURRENTS 



251 



These rays were called by the discoverer X-rays ; but 
the tendency of scientists is to call them Roentgen rays. 

398. The Dynamo. — The dynamo is a machine for con- 
verting mechanical energy into an electric current which 
has nearly the same amount of energy as that applied to 
the dynamo. It has as its basis the production of cur- 
rents by inductive effects. 

The dynamo consists of a field-magnet and an armature. 
The field-magnet is a powerful electromagnet of the 
horseshoe type ; the armature consists essentially of a 
soft iron core, surrounded by 
coils of insulated copper wire 
wound parallel to the axis of 
the core. Figure 154 represents 
the simplest possible dynamo. 
N and S represent the poles of 
a powerful magnet, and WW a 
single coil of wire arranged to 
revolve between the poles N and S. The ends of the 
wire are attached to two curved copper plates, C(7', which 
are insulated from each other, and revolve with the coil. 
B and B' are two strips of metal, called brushes., resting 
on CC . B' rests on C while W is passing downward. 

As the coil of wire revolves, it cuts the lines of magnetic 
force between the poles iV^and aS', and a current of electricity 
is induced in it, if it is a part of a complete circuit. As half 
of the coil TF moves away from aS', and toward iV, a current 
is induced in one direction, as shown by the arrow ; while, 
at the same time, the other half is moving toward S and 
aivay from iV, and thus has a current induced in the op- 
posite direction. As the parts TTand W revolve, they will 
change places ; hut the part of the coil that is making the 
lower half of the revolution will ahvays carry a current in 
one direction^ and the other part will always carry a current 




ELECTRICITY 



[§398 



in the opposite direction. The latter current will pass across 
the end and follow or unite with the current generated in the 
other part of the coil, flow to out on the brush ^, through 
the external circuit E, and back through the brush B', 

The copper plates O and C form what is called a com- 
mutator^ and the plates are called commutator segments. 
The commutator revolves with the coil, so that the seg- 
ments are successively in contact with first one brush 
and then the other, thus causing the current to flow 
always in the same direction. In actual practice there are 
a number of coils, each consisting of a number of turns of 
wire ; and a commutator segment is added for each addi- 
tional coil, the end of one coil and the beginning of the 
next being attached to each segment. 

Figure 155 is a diagram of a simple form of dynamo. 

D represents a block of iron, placed on a shaft X, upon 

which it can revolve ; <%, 5, c, and d 

r l are spools of insulated wire fastened 

j to i), so as to revolve, like the spokes 

of a wheel; J is insulating material, 
and 1, 2, 3, and 4 are commutator 
segments. The end of one coil and 
the beginning of the next are at- 
tached to each commutator segment, 
so that the spools form a complete 
circuit among themselves. B and B' 
are brushes which rest upon the oppo- 
site sides of the commutator. If a 
current passes in at B to the seg- 
ment 3, we see that it will divide, 
half passing through spool c and 
then through cZ, and half through h and then through a., and 
out at jB', the spools simply forming a shunt circuit. N 
and S are the poles of the field-magnet wound as shown. 




Fig. 155. 



§§ 396-397] 



INDUCED CURRENTS 



249 




Fig. 150. 



been made by Professor Crookes, and Fig. 150 shows one 
of the forms of glass tubes devised by him 
for this purpose. The rarefaction of air 
obtained in these tubes is such that only 
about one-millionth of an atmosphere re- 
mains. When a spark discharge from an 
induction coil, or from a Toepler-Holtz 
machine, is passing through one of these 
tubes, it glows with a peculiar pale greenish 
light ; and the path of discharge, as indi- 
cated by the light, varies with the degree 
of rarefaction. The rays may be deflected 
by magnets or reflectors, and may be brought 
to a focus at a particular point. 

397. Roentgen Rays. — In 1895, W. K. Roentgen, a 
German professor, discovered a fact which is of great 
scientific importance. He found that some of the 
Crookes tubes, when carrying a secondary current from 
an induction coil, gave off invisible rays, which caused 
fluorescent substances, tungstate of calcium, for example,- 
to glow, and also had the power of affecting an ordinary 
photographic plate. The ebonite cover in an 
ordinary plate-holder seems to transmit these 
rays, as do also flesh, cloth, paper, and many 
other substances ; while metals, bones, sticks 
of graphite, etc., seem to form an effective 
screen to the passage of the rays. By reason 
of the ability of the rays to pass through 
flesh, so-called photographs may be taken of 
the bones of the body or of foreign substances 
embedded in the flesh. For this purpose 
tubes such as the one shown in Fig. 151 are 
used. The rays are radiated from the central 
Fig. 151. disk. 




250 



ELECTRICITY 



397 



Figure 152 shows a photograph of a human hand, which 
was taken by laying the liand upon a covered plate-holder 

and exposing it for 
several moments with- 
in a few inches of 
that portion of a 
powerful Crookes 
tube which emits the 
Roentgen rays. The 
rays passing through 
the flesh affected the 
plate, while the bones 
destroyed the rays 
striking them. If it 
is desired to see the 
effects of the Roent- 
gen rays, instead of 
photographing with 
them, a fluoroscope 
(Fig. 153) is used. 
This consists of a card- 
■^^^- ■^^-- board screen, coated 

with tungstate of calcium or other fluorescent substance, 
and placed in the large end of a flaring box, while the 
other end is shaped to fit the head and ex- 
clude any side rays of light. The fluoroscope 
is placed to the eyes, the hand being held in 
front of the screen and between that and the 
tube. The shadow of the bones of the hand 
will be plainly visible, while the flesh will 
appear almost transparent. Such an appara- 
tus is now often used to locate bullets or 
other foreign substances which have in any manner found 
their way into the body. 





Fig. 153. 



§§399-401] INDUCED CURRENTS 255 

The number of volts generated in an armature coil equals 
the product of the loops in series^ the rate of change of lines 
of force passing through the coil^ and .00,000,001. 

400. The Alternator. — As already suggested, each coil 
in the armature referred to in Fig. 155 has induced in it,- 
during each revolution, two currents or electrical impulses, 
which are in opposite directions. Now, if the ends of 
these coils are attached to two insulated brass rings, instead 
of to the segments of the commutator, and the rings are 
connected to the external circuit by means of brushes, a 
series of impulses, or momentary currents, will be sent out 
upon the wires of the external circuit, first in one direction 
and then in the other. Such a current is called an alter- 
nating current., and the generator is called an alternator. 

The alternating current is fully as effective for some 
purposes as the direct, especially for lighting. Motors are 
frequently made adapted to alternating currents ; and in 
fact these currents, in many cases, are superior to direct 
currents. 

401. Transformers. — The transformer is an apparatus 
used to change an alternating current of high voltage into 
one of comparatively low voltage. The principle of the 
transformer is similar to that of the induction coil; but, 
while the latter is usually a "step-up " converter, — that is, 
produces a secondary current of higher voltage than the 
primary, — the former is a " step- 
down" converter. j- 

Figure 156 shows in diagram the i^ 
principle of the transformer. The 
primary and secondary coils sur- 
round the same iron core, the primary coil P consisting 
of many turns of fine wire, and the secondary S consist- 
ing of comparatively few turns of heavy wire. As the 
current in the primary coil is alternating, it causes a con- 




256 ELECTRICITY [§ 401 

stant rapid reversal of the polarity of the core, and so 
no circuit-breaker, such as is needed with the induction 
coil, is required in the transformer. 

In practice the laminated iron core ( C in the diagram) 
is enclosed in a heavy iron casing, so that as few of the 
lines of force as possible escape ; and the two coils are 
wound one on the other, in the same manner as with the 
induction coil. 

In this case, also, the ratio between the turns of wire in 
the coils determines the ratio between the electromotive 
forces. The electromotive force of a primary alternating 
current is frequently from 2000 to 2200 volts, and this 
is cut down to 100 or 110 volts by having the ratio be- 
tween the turns 20. For instance, if a church requires 
for lighting 100 amperes of current at 100 volts, the alter- 
nator will send 2000 volts at 5 amperes, with a ratio be- 
tween the coils of 20. In such a case, the line wires 
carrying the high voltage current are run to the building 
to be lighted, a transformer is placed upon a post outside 
the building, and from it the wires carrying the trans- 
formed current are run into the building. 

One of the principal advantages of the transformer is the 
great saving in expenses in transmitting electric energy. 
As the current which a wire will carry without heating 
injuriously depends only on the amperes, and not at all on 
the voltage, it follows that the wire which would just 
carry safely the above current at 2000 volts, would carry 
only 2^0 of the same energy at 100 volts. This becomes an 
important factor when electric energy is carried in enor- 
mous quantities many miles, as is the case at Niagara Falls 
and at other sources of water-power where electric energy 
may be generated more cheaply than with steam-power. 
In such cases the electromotive force is sometimes as high 
as 40,000 volts, transmitted for one hundred miles or more. 



§398] INDUCED CURBENTS 253 

Now, suppose that the field-magnet is a weak mag- 
net, and we cause the armature, formed by D and the 
spools, to revolve ; the coils upon the spools will cut the 
lines of force which pass from iV to aS', and currents of 
electricity will be generated in the wires upon the spools.- 
The spools a and b will be moving away from iV and toward 
S^ and will have a current generated in them from the 
inner end toward the outer, as shown by the arrows ; the 
current from a passing to segment 1, and out on B'^ while 
the current from b will pass to the segment 2, through 
a, to the segment 1, and out on B'. At the same time the 
spools c and d will be moving from S toward iV, and they 
will have a current induced in them in the opposite direc- 
tion, which will floAV from outer to inner end and from c 
to c?, as shown by the arrows ; and this current will also 
flow out upon B^. As b and d pass the middle points of 
>S' and iV, the current in them will be reversed ; that in b 
will flow forward through c to B\ and that induced in d 
will flow back to B' . 

Thus, as long as the armature is kept revolving, cur- 
rents, or rather electrical impulses, will be generated in 
the halves of the armature ; they will flow around it in 
opposite directions, and, meeting at the commutator seg- 
ment which happens to be in contact with B\ will flow 
out to the external circuit. 

As a current is generated in the armature and passes 
out to the external circuit, it shunts at B\ as shown in the 
figure. A part flows around the coils of the field-mag- 
net, making it stronger, and thus increasing the number 
of lines of magnetic force passing from iVto aS' which will 
be cut by the revolving coils of wire. This, in turn, 
increases the strength of the induced current. This goes 
on until the fields have attained their maximum strength, 
or have become saturated. 



254 ELECTRICITY [§§ 398-899 

There are two points in the field, opposite each other, 
which give the maximum inductive effect ; and as the 
coils pass these points, the current is the strongest. At 
the points halfway between these it is the weakest. So, 
as there are four coils, there will be four distinct impulses 
to each revolution of the armature. If we increase the 
number of coils, and run the armature at a high speed, 
these impulses come in such rapid succession that the 
effect is that of a steady flow. 

399. Electromotive Force of Dynamos. — The electromo- 
tive force generated by a d3aiamo depends upon the rate 
of change in number of lines of force of the field-magnet 
passing through the coils of the armature. If we have a 
wire with a single turn, or loop, and the number of lines 
passing through the loop changes at tlie rate of one per 
second, the electromotive force generated in the wire will 
be equal to .00,000,001 volt. And the total voltage of 
any coil will equal the product of this number, the loops 
in series, and the rate of change of lines through the 
loops. 

In Fig. 155 there are always two spools of wire in series; 
so the number of loops in series would be twice the num- 
ber on one spool. The number of lines passing through 
the loops would depend, of course, on the strength of the 
magnet field; and the rate at which they change would 
depend on the velocity of rotation of the armature. 

We may cover this, and other suggestions, b}^ the fol- 
lowing statement : 

When the lines of force passing through an armature coil 
are increasing^ the current is in one direction; when decreas- 
ing, it is in the other direction. 

The electromotive force of a dynamo is j^roportional to the 
number of coils in series, the strength of the field-magnets, 
and the rate of rotation of the armature. 



§402] 



USES OF CURRENT ELECTRICITY 



259 



in diagram, how this may be done. Referring to the law 
which governs the arrangement of poles of electromagnets, 
we can see that the field magnets iV and S will be north 
and south poles as shown, and as long as the current flows 
as indicated, they will remain un- 
changed. With the armature, how- 
ever, it is different ; the poles of the 
magnets are constantly reversing, 
just as is the case with the armature 
of the dynamo in Fig. 155. 

D, Fig. 158, represents the dynamo 
from which the current comes to run 
the motor. The current passes to A, 
where it shunts, a part going to the 
field magnets iV and S^ and a part to 
the brush B. From B it goes to the 
commutator segment 1, where it 
again divides, and passes around the 
spools of the armature in opposite 
directions, as shown in the diagram, making s and s' 
south poles and 7i and n' north poles. Of course the like 
poles of field and armature will repel, and unlike poles 
will attract, causing the armature to revolve as shown by 
the arrows. As n comes into the position of s, commu- 
tator segment 4 will take the place of 1, and the current 
will be reversed, changing 7^ to a south pole. And a study 
of the figure will show that a similar thing happens 
when s' takes the place of n' : it becomes a north pole. 
So we always have north poles of the armature in the 
positions from iV to S, and south poles in the positions 
from S to iV, the current always flowing in at B, divid- 
ing and flowing around n and n' in one direction and 




Fig. 158. 



through s 
brush B'. 



and s' in the opposite direction and out on the 



260 



ELECTRICITY 



[§§ 403-i04 




Fig. 159. 




Fig. 160. 



403. The Drum Armature. — Although dynamos and 
motors are sometimes made upon the plan shown in 

Figs. 155 and 158, the 
common form of arma- 
ture is the drum arma- 
ture (Fig. 159), which 
is a cylinder built up of 
circular disks of soft iron, and separated from each other 
by thin sheets of paper. This cylinder is wound from 
end to end with insulated wire, which is wound on in a 
series of coils, the ends of which are fastened to the seg- 
ments of the commutator. The commu- 
tator has as many segments as there are 
coils. When the current passes into these 
coils from one of the brushes, and out 
upon the other, it magnetizes the arma- 
ture, as shown diagrammatically in Fig. 
160, one half being a north pole and the other a south 
pole. The result is motion, as shown by the arrow ; but, 
although the armature rotates, the current always passes in 
at the same relative position, and the poles are stationar}^, 
so they are continually attracted by the opposite, and 
repelled by the like, pole of the field magnets. 

404. Methods of Winding. — There are three methods of 
winding the field magnets of motors and dynamos — series, 

shunt, and compound. 

Figure 161 shows a series-wound 
machine, where all of the current that 
passes into it, or is generated in it, passes 
through the armature and also through 
the field coils ; the two are in series. The 
current passing through the field coils 
magnetizes the field magnets. 
Fig. 161. Figure 162 represents a shunt-wound 




§ 402] USES OF CUBEENT ELECTRICITY 257 

EXERCISES 

1. If the efficiency of the dynamo is .92, how many watts 
will a 100 horse-power engine be able to supply ? 

2. If a single loop of wire is rotating between the poles of 
a horseshoe magnet at the rate of 10 complete rotations per 
second, and, at the maximum, it encloses 400 lines of force, 
what will be the average voltage generated in the loop ? 

3. What will be the average voltage if the coil has 40 loops, 
and encloses at the maximum 2000 lines ? 

4. How many times will the current reverse its direction 
during one rotation ? 

5. If there are 12 coils of 60 loops each in series, enclosing 
22,000 lines, and making 30 complete rotations per second, what 
would be the voltage ? 

6. If, in such a case, the coils were arranged in multiple 
series, with three sets in multiple, each set having four coils 
in series, what would be the voltage ? 

7. If the ratio between the coils of a step-down transformer 
were 8, and it received a current of 1000 volts, what voltage 
would it transmit ? 

8. How would it be under such circumstances with an 
ordinary step-up induction coil ? 

9. If a voltage of 40,000 is required, and 16 dynamos are 
available, each capable of generating 2500 volts, how should 
they be connected ? 

10. How should they be connected if 2500 volts were re- 
quired ? if 20,000 were required ? 



SECTION 9. PRACTICAL USES OF CURRENT 
ELECTRICITY 

402. The Electric Motor. — The electric motor is a ma- 
chine for the transformation of electric energy into mechan- 
ical energy. In construction it is very similar to the 
dynamo. In fact there is no material difference between 



258 ELECTRICITY [§ 402 

them ; any dyDamo will run as a motor, or any motor 
as a dynamo, by making some slight changes. Some elec- 
tric motors on automobiles are now arranged so that they 
may be run as dynamos by the wheels of the automobile, 
while going down hill, the electric energy generated being 
stored in the battery ; at the same time the dynamo acts 
as a brake on the wheels of the automobile. 

But while the dynamo is made to run by an outside 
force, and generates a current of electricity, the motor 
receives a current generated by a dynamo or battery, and 
produces mechanical ponder to run other machinery. It 
is often desirable to have a source of power where it is 
not convenient to have a steam-engine, or other common 
source of power ; and in such places an electric motor is 
frequently used. 

Suppose we have two bar magnets fastened together 
and mounted on a shaft so that they are free to turn 
between the poles of a strong horseshoe magnet, as indi- 
cated in Fig. 157. It is clear that the bar 
magnets will turn in the direction indicated 
by the arrows, because the poles of the 
horseshoe magnet will repel the like poles 
and attract the unlike. Here the motion 
would be only until the opposite poles were 
as close together as possible. But, suppose 
p ^-_ we had some means of reversing the poles 

of the bar magnets as they passed the poles 
of the large magnet, so the north poles of the bar magnets 
would always he in a position above the center^ and the south 
poles helow the center. Then the bar magnets would keep 
on revolving about the axis. 

By making the revolving magnets electromagnets, they 
may be so arranged that the poles will be changed at a 
certain point, and this end attained. Figure 158 shows, 





§§ 404-405] USES OF CURRENT ELECTRICITY 



261 




Fig. 162. 



machine, where the current divides, a part passing through 
the field coils and a part through the armature, if it is 
a motor, or part through the field coils 
and part through the external circuit, 
if a dynamo. In this case the two are 
in parallel, forming a shunt. 

Figure 163 shows the compound 
method of winding. In this case all of 
the current generated passes through the 
field coils. There are two of these coils, 
one a coil of fine wire of many turns, 
which is one branch of a shunt circuit, 
and the other a short coil of large wire connected in series 
with the external circuit. This is a com- 
pound of the other two, series and shunt. 
If the external resistance is high, so that 
little current will flow, a larger propor- 
tion of the current generated will flow 
through the fine field coils. But if the 
external resistance is small, a large flow 
of current will be the result, and as this 
passes through the coarse field coils, 
the field magnets will be proportionally 
stronger. In such case, even if the machine is forced 
to run slower on account of the extra load, the added 
lines of magnetic force will keep the E.M.F. nearly con- 
stant. 

For dynamos which are used to produce a constant 
E.M.F. and a variable current, as on incandescent light 
circuits, where lights are constantly being turned on and 
off, the compound method of winding is much used. 

405. The Incandescent Lamp. — If we place a piece of 
platinum or iron wire in a circuit, and pass a strong cur- 
rent of electricity through it, the wire will become white- 




FiG. 163. 




262 ELECTRICITY [§§ 405-406 

hot, and the iron may be easily melted. This represents 
the principle of the incandescent lamp. It consists of a 
carbon filament, bent into a loop, and placed in a glass 
globe from which most of the air has been exhausted. 
The filament, when the lamp is used, is heated white-hot 
by an electric current. The air is exhausted from the 
globe, as of course a filament of carbon, heated to a white 
heat in the presence of oxygen, would burn. 
Figure 164 is a sectional view of an incandescent 
lamp. 5 is a brass button, set in plaster of 
Paris, and S the outer ring, held in place by the 
same "material, forming the cap which screws 
into the socket. F^ the filament, is fastened to 
the ends of two short pieces of platinum wire, 
which are fused through the glass tube G-. The 
other ends of these wires are soldered to B and S respec- 
tively, so that when the current enters from one wire of 
the socket by a contact with B^ it passes down TF through 
F^ back through T^^ and out to the other wire of the 
socket by way of S. A study of a complete and a dis- 
sected lamp will show these connections very clearly. 

The ordinary incandescent lamp requires ^ ampere of 
current ; and as its resistance is 220 ohms, it requires a fall 
of potential through it of 110 volts. Some lamps have a 
resistance of 110 ohms and use 1 ampere. 

406. The Incandescent Lamp Circuit. — Incandescent 
lamps are connected in the circuit in parallel, as shown in 

Fig. 165 ; so if all the lamps in a . . ^ . ^ 

circuit were alike, the resistance U U [o p V_ d I 

of the lot would be the resistance ' ' 1 ' — ^^ 

of one lamp divided by the number. ^^^' ^^^''" 

Hence, according to Ohm's Law, the greater the number 
of lamps turned on, the greater the flow of current which 
must be furnished by the dynamo. The dynamo must be 



§§406-407] USES OF CURRENT ELECTRICITY 



263 



If 



IT 



so constructed that it will supply a current at a constant 
voltage, no matter what the resistance of the external 
circuit may be, and this end is attained, in most cases, 
by compound winding. A little variation in the E.M.F. 
of the current causes a decided difference in the inten- 
sity of the light given by any single lamp ; so if the light 
is to be kept constant, the voltage must be constant. 

407. The Three-wire System. — As a matter of economy 
and convenience, the three-wire system of wiring for incan- 
descent lamps is often resorted to. Figure 166 represents 
such a system. Two dynamos, D and I)\ are set up, and 
connected in series ; and, as in the case of cells, the voltage 
of the two will be twice that of one ; but a third wire, 
called the neutral wire iV, is connected as shown. Now, 
if the difference of potential between the electrodes of each 
machine is 110 volts, the difference of 
potential between the + and — wires will 
be 220 volts. If the two dynamos were 
worked upon different circuits, four wires 
would be necessary, while here only three 
are required, and the neutral wire is usually 
carrying little or no current. Suppose 
each lamp requires 1 ampere of current, 
and we have four lamps turned on between 
the -\- and the neutral wire, and three 
lamps between the — and the neutral wire. 
Four amperes of current must flow up the -j- wire to 
supply these lamps, while the other three lamps will carry 
but 3 amperes. So there will be a flow of 1 ampere 
through the neutral wire toward the dynamo, because, the 
resistance of the four being less than that of the three, 
the fall in potential through them will be less, and the 
potential between the lamps would be higher than at N if 
sufficient current did not flow to N to keep the potentials 



-^ 



U 



U 



K 



D D 



Fig. 166. 



264 ELECTRICITY [§§ 407-408 

equal. If a is now turned off, 3 amperes of current will 
flow up the + wire, and all of it will flow through the 
lamps e, /, and ^, and there will be no flow in either direc- 
tion .through the neutral wire. But suppose we turn off 
both a and 6, only 2 amperes will then be required to light 
c and c?, and 1 ampere of current will flow out on the 
neutral wire to supply the remainder of the 3 amperes 
required to light the lamps connected between the neu- 
tral and — wires. Hence, each dynamo will supply the 
current for its own brancli. 

The great expense of electric lighting is in the wiring. 
In the use of the three-wire system, one line wire is saved ; 
and if the system is properly balanced, the wires may be 
smaller, as 1 ampere of current will flow through two 
lamps, in series, and thus light two lamps instead of one ; 
and a wire will carry just as many amperes of current, 
without heating injuriously, under a pressure of 220 volts 
as under a pressure of 110 volts. 

408. The Arc Lamp. — If we place two sticks of carbon 
in series, in a circuit carrying a strong current of elec- 
tricity having a voltage of 40 or 50, touch their ends 
^ together, and then separate them about three- 
eighths of an inch, a brilliant light will be pro- 
duced. The ends of the carbons will become 
white-hot, some particles of carbon will be forced 
off, and some, no doubt, volatilized. The space 
between the ends of the carbons is called an 
"^f^ electric arc, and has the highest artificial tempera- 
ture obtainable. Figure 167 shows the arrange- 
_ ment of the carbons and the arc. The -j- carbon 
~- is the brightest; it becomes cupped out, forming 
what is called the crater, and wastes away much 
faster than the — carbon. The carbons must touch before 
the arc will form, and then the space between them 



§§ 408-410] USES OF CURBENT ELECTRICITY 



265 





^^^ 




1 






A 


M 


1 


i 

+ 
\ — 





Fig. 168. 



becomes a conductor of high resistance, owing probably to 
the vapor formed there. 

Figure 168 represents a simple form of 
arc lamp. It is so arranged, by means of 
an electromagnet, that the carbons are fed 
together automatically, maintaining the 
best distance between the ends of the car- 
bons for producing the maximum light 
with the least expenditure of energy. 

409. The Arc Lamp System. — Arc lights 
are connected in series, as shown in Fig. 
169 ; and the resistance of a system of arc 
lamps is the resistance of one lamp times 
the number of lamps, plus the resistance 
of the line wires. The resistance of the ordinary arc is 
from 4 to 5 ohms ; and a flow of from 9 to 12 amperes is 
required to light the common street lamp ; hence a volt- 
age of about 50 is required for each lamp in the system. 
In this system the flow must remain constant; so it is 
evident that the E.M.F. must vary with the number of 
lamps that are burning. When an arc lamp is turned off, 

it is simply cut out by 
making a short circuit, 
so that the current flows 
%, instead of through, it. 
A system of magnets and 
coils is so arranged that 
if a carbon is broken, or 
the lamp gets out of order, the current is automatically 
shunted through a short circuit, cutting that lamp out and 
leaving the rest of the system properly connected. 

410. The Microphone. — The microphone is an instru- 
ment for the magnifying of minute sounds. It depends 
for its efficiency upon the fact that, when certain substances 




266 



ELECTRICITY 



410-411 




Fig. 170. 



having a high resistance are placed in a circuit, a little 
pressure greatly increases their conductivity. Connect 
two plates of sheet iron to the elec- 
trodes of a cell and in series with a 
tangent galvanometer ; lay one of the 
plates upon the table ; upon it place 
a small quantity of powdered carbon, 
and upon this lay the other plate 
(Fig. 170). A very slight deflection of the galvanometer 
will probably be the result, but if a little pressure is 
applied to the upper plate, a very much greater deflection 
will result. 

Figure 171 represents one of the simplest forms of the 
microphone. It consists of a stick of carbon supported in 
depressions in two blocks of carbon c and c'. These blocks 
are connected with the poles of a cell in series 
with a telephone receiver. The slightest 
vibrations of the air or the microphone will 
cause a variable pressure upon the carbon 
stick, so that any slight sounds made near 
the instrument will be greatly magnified if 
the receiver is held to the ear. The tick of a watch laid 
upon the instrument will sound very loud, and even the 
sounds made by a fly walking upon it may be distinctly 
heard. 

411. The Telephone Receiver. — Figure 172 represents 
in section the common form of the telephone receiver. It 
consists of the hard rubber case, with which we are all 

more or less familiar, 
with its concave end, 
which is placed over the 
ear. The working part 
consists of a bar magnet 
J., composed of rather 




Fig. 171. 




§§ 411-412] USES OF CURRENT ELECTRICITY 



267 



soft steel, around the end of which is wound a coil c of 
fine insulated wire, thus making it an electromagnet. 
In front of the magnet is placed a circular diaphragm of 
soft iron, which is held firmly in place close to the end 
of the magnet, but so that its center is more or less free 
to vibrate. The ends of the coil are attached to binding- 
posts at the farther end of the receiver. If the receiver 
is attached to a circuit passing through a microphone, 
so that a variable current passes through c, the strength 
of the magnet will vary and thus attract the diaphragm 
with varying force and cause it to vibrate. So if the 
ear is held to the instrument the vibrating diaphragm will 
cause vibrations of the enclosed air, and thus a sensation 
of sound. If the current passing through the receiver 
is an alternating one, the impulses in one direction will 
weaken the magnet and the impulses in the other wjll 
strengthen it and produce the same result, but somewhat 
more intensely. 

We will discuss the telephone more fully under Sound. 

412. The Telephone System. — A complete telephone 
system for two stations consists of a transmitter and a 
receiver at each station, and is represented in diagram in 




Fig. 173. The transmitter T consists of a mouthpiece M^ 
back of which is fastened a diaphragm similar to the one 
in the receiver ; back of this, and resting lightly against 
its center, is a piece of platinum P, called the contact piece. 



268 ELECTRICITY [§ 412 

This rests, in turn, against a button of carbon C. One 
wire from a cell is attached to the contact piece P and the 
other to the carbon button. The transmitter is connected 
in series with the primary coil of an induction-coil trans- 
former, forming a sensitive microphone. The secondary 
induction-coil is connected with the line wire, and in 
series with the receiver. 

Now suppose a person at station A holds the receiver 
to his ear, and another speaks into the transmitter at sta- 
tion B. As the sound-waves strike the diaphragm of the 
transmitter they cause it to vibrate, and thus cause rapid 
variations of the pressure upon the button. This, in 
turn, causes rapid and corresponding variations in the 
flow of the primary current. Every variation of the 
primary current causes a variation of the number of lines 
of force cutting the secondary coil, and this, of course, will 
induce currents in this coil. An increase of lines of force 
in the induction-coil will cause a current in one direction, 
which, we will say, strengthens the magnet in the receiver 
at A ; and a decrease of lines of force will cause a current 
in the opposite direction, which, of coarse, will weaken the 
magnet. This variation of the strength of the magnet in 
the receiver will cause a corresponding variation in its 
attraction for the diaphragm, and cause it to vibrate 
exactly as the diaphragm in the transmitter at B vibrates, 
thus reproducing the sounds causing the primary vibra- 
tions. 

One purpose of the induction-coil is to raise the electro- 
motive force of the varying current which passes through 
the transmitter, thus enabling it to become sufficiently 
effective through the resistance of the long line wires. 
The ratio between the turns of the two coils is usually 
about ten ; so the force becomes ten times greater. An- 
other purpose is to transform the varying direct current 



§§ 412-414] USES OF CURRENT ELECTRICITY 269 

into an alternating current, and thus increase its effect on 
the receiving magnet. The coil resembles more a trans- 
former than an induction-coil, as no automatic circuit- 
breaker is required. 

413. Electric Waves. — It has been found that when an 
electric discharge takes place, a disturbance is set up in 
the ether, which travels outwardly from the spark, in the 
form of a wave of disturbance, just as a water wave travels 
outward when any disturbance is set up on the surface 
of the water. The electric disturbance is called electric, 
or Hertzian, waves. These waves were discovered by 
Professor Hertz, of Germany, in 1888. 

A simple experiment shows the effects of the waves : 
If a brass ring, of about 30 cm. radius, is opened at one 
place, with the ends of the wire terminating in small balls, 
a millimeter or less apart, it forms a detector for the elec- 
tric waves. If the detector is held in front of a static 
machine, or an induction-coil, every time a spark passes 
between the poles of the machine a small spark will pass 
between the balls of the detector. 

Hertz and others have carried out many interesting and 
valuable investigations in reference to these waves ; but 
they are beyond the scope of this work. This wave effect, 
however, is the basis of the experiments in wireless teleg- 
raphy which have been carried on by Marconi and others, 
and also of such practical applications of wireless teleg- 
raphy as have been made. 

414. Wireless Telegraphy. — Evidently, if an electric 
wave is sent out whenever an electric discharge occurs, 
and this wave can be detected at a distance from the 
transmitter, messages may be sent and received by this 
method just as with wires. The detector described above, 
however, is affected sufficiently by the waves only when 
within a few meters of the discharging apparatus. So 



270 



ELECTRICITY 



[§414 



another method of detecting the waves has been adopted. 
This depends on the fact that the resistance of fine metal 
filings is enormously diminished by electric waves. If a 
glass tube, partly filled with filings, called a coherer^ is 
connected, as indicated in Fig. 174, in series with a cell 
and a telegraph sounder, no current of consequence will 
pass through the tube, if the filings are not too closely 
packed. But if a wave strikes the wire of the coherer, it 
so affects the filings that they become a good conductor, 
and the current passes through, and causes the sounder to 
click. 




Fig. 174. 



For practical purposes, however, the effect of the wave 
must be intensified. This may be done by attaching to 
one wire of the coherer a vertical wire, with one end con- 
nected with the earth and the other extending upward to 
a height depending on the distance the message is to be 
transmitted. Or the same result is reached if two metal 
plates of uniform size are connected, respectively, to the 
two wires of the coherer, the discharger of the transmitter 
being arranged in the same manner. For long distances 
vertical wires are used, with metal plates attached to the 
tops of the wires. 



416] 



USES OF CUUBENT ELECTRICITY 



271 



415. Wireless Telegraph System. — Figure 175 shows the 
entire system, such as is used in telegraphing without 
wires. B is the battery of the transmitter, whicli charges 
the induction-coil J; ^is the contact key, which regulates 
the sparks of the coil ; B the discharging apparatus, called 
the oscillator, with its wires W extending upward a hun- 
dred feet or more and W connecting with the earth ; B' is 
the battery of the receiver ; R an ordinary telegraph relay ; 
6' the coherer, with its wires W" W" similar to TTand W ; 
B" the battery which actuates, through the coherer, the 




relay ; aS' the sounder; and E an ordinary bell, used as a 
decoherer, which is in parallel with the sounder, and should 
be muffled or have the gong removed. 

When the contact key is closed, the current enters the 
coil, and a spark passes across the balls of D. This sends 
out an electric wave which, affecting the wires W'\ causes 
the filings in the coherer to become conductive. This 
allows the current to flow through the coherer and close 
the relay, which in turn allows a current to flow from B' 
to the sounder, and cause it to click. At the same time 



272 ELECTRICITY [§ 415 

the hammer of the bell or the trembler, as it is called, is 
caused to strike the coherer and thus destroy the con- 
ductibility of the filings by jarring them apart. 

To produce the best results the relay should have but 
little self-induction, and should have a very high resist- 
ance, as high as 1000 ohms. The sounder and the trem- 
bler should have equally high resistances. The filings 
should be of rather course hard nickel with a little hard 
silver and a trifle of mercury. The metal plates at the 
tops of the vertical wires should be of the same size and 
substance. 

In sending messages it is only necessary for the sender 
to work the contact key as he would with the ordinary 
telegraph system, and the signals will be received from the 
sounder in the usual manner. By the use of enormous 
electric currents and a large number of vertical wires ex- 
tending upward long distances, messages have been sent 
across the Atlantic ocean a distance of two thousand miles 
or more. But, except to cross the ocean, it is doubtful if 
practical application will be made of the principle between 
stations more than a few hundred miles apart. 

EXERCISES 

1. Three electric bells are connected in parallel. The resist- 
ance of each bell, including the wire connecting it with the 
line wires, is 3.2 ohms. The resistance of the line wires is 
.5 ohms, and the internal resistance of the battery is 3 ohms. 
What is the total resistance of the circuit ? 

2. A telegraph line 5 miles long is made of iron wire 204 
mils in diameter. Find its resistance. 

3. The line in Exercise 2 failed to work and the operator at 
one end found that the part with which he was connected 
had a resistance of 2 ohms. How far from his end was the 
" ground " ? 



USES OF CURRENT ELECTRICITY 273 

4. Draw a diagram showing how 6 electric bells may be 
connected to ring by means of a single push-button. 

5. Twenty arc lamps are connected in series, each lamp 
having a resistance of 4.5 ohms. The line wire has a resist- 
ance of 4 ohms and the dynamo has an internal resistance of 
2.2 ohms. If a current of 9.5 amperes must be maintained, 
what must be the voltage of the dynamo ? 

6. A dynamo armature is wound with No. 8 wire, the safe 
carrying capacity of which is 23 amperes. It furnishes a cur- 
rent at an E.M.F. of 110 volts. How many 16 candle power 
lamps, each having a resistance of 220 ohms, may be safely 
lighted by this dynamo ? 

7. Sixteen arc lamps m series are connected with a dynamo 
by means of a line wire having 6 ohms resistance. If the E. 
M.F. of the current furnished is 703 volts and the flow is 9.5 
amperes, what is the resistance of each lamp ? If one lamp is 
cut out, what change in voltage will be necessary to keep the 
flow constant ? 

8. A dynamo is connected to an engine. If 15% of the 
power of the engine is wasted by friction, etc., what must be 
its horse power to run the dynamo when lighting 550 incan- 
descent lamps, each carrying 1 ampere of current and having 
a resistance of 110 ohms ? 

9. Two arc lamps requiring a voltage of 40 and a flow of 10 
amperes are placed in series between the terminals of a 110- 
volt dynamo. What resistance must be placed in series with 
them to make them run properly ? 

10. If 75 incandescent lamps, each requiring i ampere of 
current, are connected on one side of a three-wire system and 
89 similar ones are burning on the other, what will be the 
direction and the amount of flow through each of the three 
wires if the smaller number of lamps are connected between 
the positive and neutral wire ? 



CHAPTER VIII 

SOUND 

SECTION 1. CAUSE OF SOUND 

416. Sound. — Every one is familiar with what is ordi- 
narily spoken of as sound ; it is simply the noise made by 
innumerable things about us, — the rumbling wagon, the 
falling book, the swinging bell, musical instruments, the 
organs of the voice. 

417. Sonorous Bodies. — The wagon, the book, the bell, 
which produces the sound, is called a sonorous body. In 
general, any object which is primarily the cause of sound 
may be called a sonorous body. I 

418. Motion of Sonorous Bodies. — When the wagon pro- 
duces sound, it is in motion ; it is the same with the book, 
or the bell, or with any sonorous body. In fact, whenever 
sound is produced it is due to the motion of the sonorous 
body, but it is evident at once that not every moving body 
will produce sound. The hand moved slowly through the 
air produces no sound ; the falling book causes no sound 
as it falls, but only on striking. So we must distinguish 
between motions that produce sound and those that do not. 

419. Vibratory Motion. — In the first place, to produce 
sound the motion must be vibratory — that is, like the 
swinging of a pendulum, back and forth, repeating the same 
motion continually. When a guitar string is pulled for- 
ward and released, it springs back past its normal position 
to the other side, then springs forward, and then repeats 

274 



§§416-422] CAUSE OF SOUND 275 

its motion back and forth until it finally comes to rest. 
Such motion is called vibratory ; and it will be found that 
all sonorous bodies have such motion. Placing the ends 
of the prongs of a sounding tuning-fork in water, the 
splashing of the water indicates the vibrations of the 
prongs. The large wires of a piano may be seen to 
vibrate back and forth as they sound ; and the rim of a 
sounding bell may be shown to be vibrating by holding 
against it a suspended pith ball. 

420. Molecular Vibration. — If a piece of iron is struck 
with a hammer, sound will be produced ; not because the 
iron or the hammer vibrates as a whole, but because the 
molecules coming in contact are driven aj^art into the iron 
and the hammer, and they then spring back and vibrate 
for a short time about their normal positions. And it 
is this vibration of the molecules^ and not of the mass, 
which in such cases causes sound. 

421. Frequency of Vibration. — It will readily be seen, 
however, that not every vibratory motion, whether of 
masses or of molecules, causes sound. The vibrations of 
a pendulum do not ordinarily cause sound, neither do the 
vibrations of molecules which cause heat. And investi- 
gation shows that, to cause sound, the vibrations must 
be neither too slow nor too fast. The number of vibra- 
tions per second is called the frequency of vibration. So 
we may say the frequency of the vibration must be within 
certain limits in order to cause sound. 

422. Range of Frequency. — If the frequency is less 
than about 20 per second or more than about 40,000, no 
sound will be produced, because the rate of vibration is 
too slow or too fast to produce any effect on the ear. 
Hence the range of frequency which is capable of pro- 
ducing sound is between about 20 and 40,000 vibrations 
per second. 



276 SOUND [§§ 423-426 

423. Cause of Sound. — From the foregoing we may 
assign as the cause of sound, an^/ body or set of molecules 
which has a sufficiently rapid vibratory motion. 

SECTION 2. PROPAGATION OF SOUND 

424. Propagation of Sound. — Evidently tlie ear can 
perceive sound only when the effect of the motion of the 
sonorous body is transmitted from the sounding body to 
the ear, and the transmission of this effect is called the 
propagation of sound. 

425. Sound Media. — In order to propagate sound there 
must be some medium through vrhich it is pro23agated; 
there must be some substance existing between the sound- 
ing body and the ear which carries the effect from one to 
the other. The usual medium for such purposes is the air ; 
but it may be any gas or liquid, or almost any solid. In 
fact, any elastic substance may be used as a sound medium. 
For instance, when the ear is under water, two stones 
struck together under the water sound even more distinct 
than when in air ; or if a hot-water pipe in one part of a 
building is tapped lightly with a piece of iron, the sound 
may be distinctly heard in any room where the pipes 
extend. 

To show that some medium is required to propagate 
sound, it is necessary only to place in a vacuum a sonorous 
body resting on some non-elastic substance, and then no 
sound will be heard. 

426. Manner of Propagation. — When an iron bar is 
tapped at one end, and the sound is heard through the 
iron at the other end, it is evident that no portion of the 
iron moves from one end of the bar to the other in order 
to convey the effect of the tap. Similarly, when a whistle 
blows, it cannot be possible that the air moves from the 



§§426-428] PROPAGATION OF SOUND 277 

whistle in every direction as far as the whistle can be 
heard, often several miles. On the contrary, it has been 
conclusively shown that none of the molecules between 
the sonorous body and the ear, while propagating the 
effect, move for any great distance from their normal 
places. But instead the effect is passed along from one 
set of molecules to another — the sonorous body causes a 
disturbance among the surrounding molecules, and the dis- 
turbance is passed along to the ear. To understand more 
clearly the manner of this propagation, we may consider 
the propagation of disturbances in water. 

427. Wave-motion. — When a pebble is dropped in quiet 
water, it causes a disturbance on the surface of the water 
which travels outward as a constantly enlarging circle, 
or wave. The molecules of water where the stone strikes 
are driven outward and upward; this affects neighbor- 
ing molecules, and the effect is thus passed along from one 
set of molecules to another. If two stones are struck 
together under water, they set up a somewhat similar 
disturbance among the surrounding molecules ; and this 
disturbance is propagated outward in the form of a 
constantly enlarging spherical shell, or wave. And if 
the disturbance reaches the ear, it causes the effect called 
sound. 

The movement of the disturbance, in either of these 
cases, is called wave-motion ; and it is always by wave- 
motion that sound is propagated, each vibration of the 
sonorous body sending out a distinct wave. 

428. Crests and Troughs. — If a piece of wood is float- 
ing on the water, when a wave passes the wood, instead of 
moving outward with the wave, the wood merely rises 
and then falls without otherwise changing its position. 
This is due to the fact that the molecules of water merely 
rise and fall ; the wave, which is just a special arrange- 



278 SOUND [§§428-430 

ment of the molecules, being that which travels outward. 
So we have a constantly enlarging circle of raised mole- 
cules, followed by one of depressed molecules. The raised 
portion of the wave is called its crest and the depressed 
portion its trough. 

429. Sound-waves. — In order to form a conception of 
sound-waves, let us consider a long bar of steel. If such 
a bar is tapped on one end with a hammer, it is probable 
that the molecules which come in contact with the hammer 
are driven in toward the other molecules, but at once 
bound back ; inertia, howevei^ carries them' back beyond 
their normal positions, and thus they vibrate back and 
forth, the amplitude of the vibration rapidly decreasing 
until they come to rest. But when first driven in, the 
molecules come in contact with the neighboring molecules, 
and drive these, in their turn, farther in the steel. This 
second lot of molecules also then vibrates back and forth 
across its normal position. But these molecules, in their 
turn, have similarly set vibrating a third set of molecules, 
and this effect is thus continued throughout the entire 
length of the bar. 

The vibratory disturbance which is set up at one end of 
the bar and travels to the other is a series of sound-waves r 
If the ear were held near the farther end of the bar, the 
sound of the blow could be heard much more distinctly 
than if the sound medium were the air instead of the 
steel. 

430. Condensations and Rarefactions. — It is evident 
that, when the first set of molecules strikes against the 
second, there is formed a momentarily condensed portion 
of steel. And then, as the two sets spring apart, a rare- 
fied portion is formed. It is also evident that this will 
be the case all along the bar ; there will be a dense portion 
where the neighboring sets of molecules come together. 



§§ 430-432] PROPAGATION OF SOUND 279 

and this will instantly be followed by a rare portion. 
These conditions of the molecules are called the con- 
densations and rarefac- 
tions of the sound-waves. '' ^;"C.§S'''" 
Figure 176 gives an idea ' ;_? ,"'Ji i' 
of this effect with a sound- ^' ,,^ ,;l';;;',„[',:,; 
ing body producing waves ; ,|" ''§j!;j;i;J!i': 
m air. .'^s#^ '''nH!'!;!;. 

431. Transverse and ^f|^^__ _ ^^^^,^^ , ,J0^ 
Longitudinal Vibrations. — "" f i76 

In case of a water-wave on 

the surface of the water the particles of water merely rise 
and fall — vibrate up and down — as the wave passes 
along. In such cases the vibrating particles cross the 
line in which the wave is moving, and this is called a 
transverse vibration. With the sound-wave, however, the 
molecules vibrate along the line in which the wave is 
moving, and this is called a longitudhial vibration. With 
the bar of steel, for instance, the sound-wave travels 
along the bar, and, as we have seen, the molecules vibrate 
longitudinally with reference to the bar. 

432. Properties of Sound Media. — In order to propagate 
sound, the medium must be sufficiently elastic to cause the 
molecules to bound apart when they are driven together 
by the vibrating sonorous body ; and such elasticity is 
the only requisite. So any elastic substance may act as a 
sound medium. 

Elasticity is not only necessary to propagate sound at 
all, but it affects the velocity of the sound, as we shall see 
later. And the only other property of the medium which 
affects the propagation of the sound materially is density. 

It is immaterial, however, what the elasticity or density 
of the medium may be so far as the manner of propagation 
is concerned ; in every case longitudinal waves of conden- 



280 SOUND [§§432-436 

sations and rarefactions travel through the medium to the 
ear, or to some other medium which reaches the ear. 

433. Direction of Propagation. — In passing from one 
place to another, unless interfered with, sound-waves travel 
in perfectly straight lines, but in ever 7/ direction from the 
source. In air, for instance, we may liken the wave to a 
sphere, the sonorous body being at the center of the 
sphere, the disturbance travelling outward along an infi- 
nite number of radii of the sphere, and each distinct wave 
being a constantly enlarging spherical shell concentric 
with the sphere and each of the other waves, as indicated 
in Fig. 176. 

434. Reflection of Sound. — If a sound-wave strikes a 
surface, like a stone wall, it bounds away from the sur- 
face, just as a ball would do. As the wave is due to the 
motion of the molecules in a line along which the wave 
travels, just as the motion of a ball is in a line along 
which the ball travels, so each molecule bounds away from 
any surface which it strikes, just as a ball would do. 

435. Echo. — If the direction in which the wave is 
travelling is perpendicular to the wall which it strikes, the 
wave will be reflected back in exactly the opposite direc- 
tion, and will travel back to its original source. So that 
any persons standing where, for instance, a gun is fired, 
will hear not only the original report but also a second 
report, called the ecJio^ which is due to the reflected wave. 

436. Speed of Propagation. — The distance which a 
sound travels in one second is its speed of propagation. 
It is said that Newton determined this by stamping his 
foot at one end of a long corridor and noticing the time 
it took for the echo from the other end to return ; the 
determination, hoAvever, could not have been very accu- 
rate, as the time was too short. 

Perhaps the most accurate measurements have been 



§§436-440] PROPAGATION OF SOUND 281 

made in the following manner : Two persons are situated 
a considerable distance apart, one mile perhaps, but in 
view of each other ; one discharges a gun, and the other 
notices the time that elapses from the time the flash is 
seen until the report is heard. As, for such a short dis- 
tance, the passage of light may be taken as instantaneous, 
the speed of the sound is, of course, the distance divided 
by the time. To eliminate the effect of the wind, a gun is 
discharged successively from each station and the time 
noted at the other, the mean of the two times being taken 
as the correct time. 

The speed in many other media has also been accu- 
rately determined, as indicated in the table, page 375, but 
the methods used are somewhat complicated. 

437. Law of Speed. — Such experiments have shown 
that when a sound-wave travels in any medium, its speed 
varies directly as the square root of the elasticity and in- 
versely as the square root of the density of the medium. 

438. Effect of Temperature on Speed. — In air at 0° 
the speed of sound-waves is 332 m. per second. But as 
the temperature rises, the air becomes less dense while the 
elasticity remains the same ; hence a rise in temperature 
increases the speed. It has been found that the speed 
increases .6 m. for each degree rise in the temperature. 

439. Effects of Pressure on Speed. — The speed in air is 
independent of changes in pressure, because as the press- 
ure increases, while the elasticity increases, the density 
correspondingly increases, so that the speed is unchanged. 

Hence, in determining the speed of sound-waves in air 
the temperature of the air must always be considered, but 
the barometer reading is immaterial. 

440. Perception of Sound. — So far we have considered 
merely sonorous bodies and their effects on surrounding 
media. But in order- that we may hear sound, the effect 



282 SOUND [§§ 440-441 

of the sonorous body must be propagated, not only to the 
ear, but through the ear, and along the auditory nerve to 
the brain. The passage along the auditory nerve is a 
subject for physiology ; but the effect on the ear is a proper 
"subject for physics, and will be considered further along. 

441. Experimental Evidence. — The substance of this 
section may be very satisfactorily shown by means of a 
sensitive flame. Such a flame may be produced by re- 
placing the ordinary gas-jet with one issuing from a pin- 
hole, — a drawn-out glass tube does nicely, — and then 
allowing the gas to pass through an ordinary wire gauze 
placed an inch or so above the opening of the tube. If 
the gas is lighted only above the gauze, the flame will be 
very sensitive ; and if two pieces of iron are struck 
together in its neighborhood, producing a loud click, the 
flame will be decidedly affected. If it is sufliciently sen- 
sitive, it may easily be extinguished in this way, even 
when the sound produced is many feet away ; and it will 
plainly be affected through long distances, and even 
through closed doors. 

This experiment conclusively shows sound to be a dis- 
turbance set up in the air by the sonorous body, the 
disturbance travelling outward as an impulse, or wave, 
affecting surrounding bodies, causing, when it affects the 
ear, the sensation ordinarily called sound. 

EXERCISES 

1. What is the frequency of a body vibrating 768 times in 8 
sec. ? 12,480 times in 4 sec. ? 15 times in a min. ? 

2. If a body vibrates 720 times in 12 sec, would it be a so- 
norous body ? If it vibrates 480,000 in 10 sec. ? in 10 min. ? 
in 10 hr. ? 

3. At the same pressure oxygen is 16 times as dense as 
hydrogen. What would be the relative speeds^f sound in the 
two gases ? 



§§442-443] VARIATIONS IN SOUNDS 283 

4. What would be the relative speeds if the pressure on the 
hydrogen was 16 times that on the oxygen ? 4 times ? 

5. If the pressure on the air is 7.3 times as great in one case 
as in another, what will be the relative speeds of sound ? 

6. What is the speed in feet of sound, if an echo is heard by 
the sportsman, from a cliff 1680 ft. away, 3 sec. after he fires 
his gun ? 

7. What is the increase in speed because of increase in 
temperature, if the cliff is 2530 ft. away and the echo is 
heard in 4.6 sec. when the temperature is 5°, and in 4.4 sec. 
when it is 10° ? 

8. What is the distance in meters from a cannon if the 
report is heard 4 sec. after the flash is seen, and the tempera- 
ture is 0° ? when it is 12° ? when it is 6S° F. ? 

9. What is the speed of sound in feet per second in air at 
0° ? What is the increase in feet per second for each degree 
increase in temperature ? 

10. How long will it take sound to travel 2 mi. when the 
temperature is 20° ? when the temperature is 20° F. ? 

11. If, when the temperature is 10°, a cannon-ball, fired with 
a horizontal velocity of 676 m. per second, is heard by the gun- 
ner to strike the target 6 sec. after he fires the cannon, what is 
the distance to the target ? 

SECTION 3. VARIATIONS IN SOUNDS 

442. Variations in Sounds. — There is a great variety of 
sounds ; scarcely do we have two sounds that are exactly 
alike, — some are louder than others, some higher, some 
more musical. In a general way, however, all the differ- 
ences between sounds may be classed under three heads : 
differences in intensity^ in pitchy and in quality. We will 
consider each of these in the order named. 

443. Intensity. — We may have two sounds apparently 
alike except that one is louder than the other ; they differ 
in loudness. Differences in loudness are due to differences 



284 SOUND [§§ 443^45 

in intensity of the sound-wave. Loudness refers to the 
sensation perceived by the ear; intensity to that which 
produces the sensation. Let us consider the cause of dif- 
ferences in intensity. 

444. Energy of Sound-waves. — Tlie intensity of a sound- 
wave depends on the amount of energy it contains. Thus, 
when a tuning-fork is set vibrating, it imparts to the 
surrounding molecules a certain amount of increased mo- 
tion; and as we have seen under heat, by virtue of this 
increase in motion the molecules have increased kinetic 
energy. This energy is passed along to the neighboring 
molecules in the form of a sound-wave, until it reaches the 
ear. The sound-wave then imparts its energy to the ear, 
and the amount of energy thus imparted determines the 
intensity of the sound. The loudness depends on the 
intensity and also on the condition of the ear — a deaf 
person would hear nothing. But the intensity depends 
only on the energy of the wave. 

So, just as energy is radiated through space from a hot 
body by means of heat-waves, so energy is radiated through 
the sound medium from a sonorous body to the ear or else- 
where by means of sound-waves. 

There are various factors which affect the amount of 
energy of sound-waves, and these we will consider sepa- 
rately. 

445. Area of Vibrating Surface. — If the handle of a 
vibrating tuning-fork is placed vertically upon a table, the 
sound will be greatly increased. This is because the fork 
causes the board to vibrate in unison with itself, and the 
greater area of the board affects a correspondingly greater 
number of molecules of the surrounding air, imparting 
more energy to the sound-wave. If the vibrating surface 
is quite small, the molecules simply pass around the sur- 
face without being caused to vibrate to any extent, and no 



§§ 445-148] VARIATIONS IN SOUNDS 285 

sound is heard. This is the case with many stringed 
instruments, so sounding-boards are required to make the 
sound audible. 

446. Amplitude of Vibration. — If a tuning-fork is struck 
harder at one time than at another, the prongs will be 
caused to vibrate farther — the amplitude of vibration will 
be greater — and the sound will be louder » This is not 
due at all to increased frequency of the vibration, but 
simply to increased amplitude. We have seen (Art. 119) 
that the vibrations of a pendulum are isochronous whether 
the amplitude is large or small ; and this is true of all 
vibrating bodies. But the greater the amplitude the 
greater the distance to be travelled in the same time, and 
necessarily the greater the velocity and therefore kinetic 
energy imparted to the molecules of the sound-wave. 

So the intensity of the wave increases with the ampli- 
tude of vibration of the sonorous body and also of the 
molecules of the medium. 

447. Effect of Density of Medium. — Evidently the denser 
the air surrounding the vibrating body, the greater the 
amount of energy imparted to it, because the number of 
air molecules affected will be proportional to the density 
of the air. Hence the denser the medium, the greater the 
intensity of the sound. 

Because of this, sounds are louder when the barometer 
is high. On cold, dry days in winter sounds are much 
louder than on warm, moist days, because the air is denser. 
Pistol-shots on mountain tops are very faint. The sound 
in the water of two stones struck together under the water 
is very intense. The tap of a hammer on an iron pipe may 
be heard distinctly through the iron at a distance of many 
blocks. 

448. Distance. — As the sound-waves travel outward 
from the sonorous body in the form of constantly enlarg- 



286 SOUND [§§ 448-451 

ing spherical waves of molecular disturbance, the surface 
of the disturbance constantly increases, and the number of 
molecules increases proportionally to the surface. Con- 
sequently, the energy being spread over more and more 
molecules, the greater the distance of the ear from the 
source the less will be the energy in the air per unit 
volume, and hence the intensity of the sound-wave that 
affects the ear will be less. When a sound-wave is a con- 
siderable distance from the sonorous body, the intensity 
increases inversely nearly as the square of the distance 
increases. 

449. Summary. — From the foregoing we find that 
sounds differ from each other in intensity; the cause of 
this difference is the amount of energy involved; the 
energy increases with the area and the amplitude of the 
vibrating body, and with the density of the surrounding 
medium ; and it increases inversely nearly as the square 
of the distance the sound-wave has travelled. 

450. Pitch. — Sounds differ also in pitch ; that is, some 
are high, or acute, while others are low, or grave. While 
intensity depends upon the energy imparted to the ear by 
the sound-wave, pitch depends upon the rate with which 
the waves strike the ear, — that is, the number striking it 
per second, — the frequency of the waves. And as a wave 
is set up by each vibration per second of the sonorous 
body, pitch depends upon the number of vibrations per 
second of the sonorous body. As the molecules of the 
medium vibrate in unison with the sonorous body, we may 
say: Pitch depends upon the frequency of the sonorous 
body, or of the molecules of the medium, or of the sound- 
wave. 

451. Numerical Value of Pitch. — As pitch depends only 
on the frequency, we may conveniently express different 
pitches in terms of their frequencies, Thus a tone with a 



§§451-454] VARIATIONS IN SOUNDS 287 

pitch of 212 is produced by a body having a frequency 
of 212 vibrations per second. 212, then, is the numerical 
value of the pitch. 

452. Frequency of Wires. — Evidently whatever affects 
the frequency affects the pitch proportionally, and in dis- 
cussing variations in pitch we need only consider varia- 
tions in frequency. A simple form of a sonorous body is 
a vibrating string or wire ; so we will consider briefly the 
laws which pertain to the frequency of vibrating wires. 

453. Effect of Tension on Frequency. — The tension of a 
wire is the tightness with which it is drawn. The greater 
the tension, the greater the elastic force which tends to 
bring the wire back when it is pulled to one side ; conse- 
quently the greater the velocity with Avhich it is brought 
back, and the greater the frequency. We have seen that 
the frequency of a pendulum varies directly as the square 
root of the force of gravity which actuates the pendulum, 
and careful experiments have shown that the frequency of 
a wire increases directly as the square root of its tension, 
which is the force actuating the wire. 

454. Effect of Mass on Frequency. — Evidently the 
greater the mass of the wire the slower it will move, if the 
tension, or elastic force, remains the same, as the force has 
more inertia to overcome. So the frequency decreases as 
the mass increases. 

The mass may be increased by increasing the diameter, 
or the length, or the density of the wire ; and it has been 
found that the following law holds with reference to 
vibrating wires or strings : 

Freqiieyicy increases inversely as the length, or the diame- 
ter^ or the square root of the density of the ivire or string. 

Application is made of these facts in the manufacture 
of musical instruments, especially pianos. Those wires 
which are to produce high notes are short, small, and 



288 SOUND [§§ 454-457 

tightly stretched, while those intended for the low notes 
are long and large, many of them being weighted, and are 
less tightly stretched. In tuning instruments, however, 
in order to secure the right pitch, the only change that 
is made ordinarily is to increase or decrease the tension. 

455. Quality. — Sounds differ also in quality^ or timbre. 
It is not difficult to distinguish between the quality of a 
guitar and a violin tone, even when of the same pitch and 
intensity. Each is caused by a string vibrating, and the 
strings may be of similar material and equal lengths and 
tensions, and still the difference in quality may be quite 
apparent. In order to understand the reason for this, we 
may consider somewhat more in detail the vibrations of 
strings and the resulting tones. 

456. Fundamental Vibrations. — The length of the string 
referred to in Art. 454, is the length between two points 
where the string is held fast, such as a and h in Fig. 177, 

and not the entire length 

yT\~~"- ""^A\ ^^ ^-^^ string. And the 

laws of vibration given 
refer to the vibration of 
the entire string between these two points. Such vibra- 
tion of the string as a whole between two such fixed points 
is called the fundamental vibration. It is indicated by 
the dotted lines in the figure. 

457. Partial Vibrations. — But certain parts of the string 
between the points a and h may vibrate at the same time 
that the entire strinof 

vibrates. Thus the °^S^£ill_f ^_I::I^^^ 

vibrations may be as / \ ^^~~~-'^^^I^>^**^""''' / \\ 

indicated by the dot- ^ — '—^ -^— ^ — -^ 

ted lines in Fig. 178. ^'°- ^^^• 

As the entire string vibrates, the portions ac, cd, and dh 

may vibrate just as if c and d were fixed points. The 



§§457-460] VARIATIONS IN SOUNDS 289 

vibrations of ac^ cd^ and dh are partial vibrations. In case 
of almost all vibrating bodies, we have the partial vibra- 
tions in conjunction with the fundamental vibration. 

458. Fundamental Tones and Overtones. — Necessarily 
the fundamentals are slower than the partials, and hence 
the pitch of their tones is lower. The tone given out 
by the fundamental vibrations are called the fundamental 
tones, and those of the partial vibrations are called over- 
tones. 

459. Effect of Tones on Quality. — The quality of any 
tone is determined altogether by its overtones. All fun- 
damental tones of the same pitch and intensity sound 
alike ; but as the overtones usually vary with different 
sonorous bodies, the combination of the overtones with the 
fundamental causes the characteristic qualities of the dif- 
ferent sounds. The fundamental, however, always con- 
trols the pitch, as it is the preponderating tone. 

460. Summary. — We have, then, sounds differing in 
intensity, in pitch, and in quality. 

Differences in intensity are due to differences in the 
amount of energy in the sound-wave. 

Differences in pitch are due to differences in frequency 
of the vibrations of the sonorous body, or of the sound- 
waves. 

Differences in quality are due to differences in the over- 
tones which combine with the fundamental to form the 
entire tone. 

EXERCISES 

1. Considering a soimd-wave as a s^jherical shell, how much 
larger will its surface be when the radius of the shell is 100 ft. 
than when it is 50 ft. ? 

2. In such case what would be the relative number of 
molecules in the two waves ? 



290 SOUND [§461 

3. If the energy imparted to the wave travels outwardly 
without loss, and is uniformly spread over the surface of the 
wave, what would be the relative amounts of energy on a unit 
surface in the two cases ? 

4. What would be the relative amounts entering the ear if 
the ear at one time was 50 ft. and at another 100 ft. from the 
sonorous body ? 

5. What would be the law, then, connecting the intensity 
of sound with the distance the wave has travelled ? 

6. A steel wire No. 25 vibrates 256 times per sec. What 
would be the frequency of a steel wire No. 30, of the same 
length and tension ? 

7. If the tension of a string at one time was 80 kg. and at 
another 20 kg., what would be the relative frequencies ? 

8. If one string is 93 cm. long and another similar one is 
37 cm. long, how many times faster will one vibrate than 
the other ? 

9. If one wire is copper and another one is iron, and 
they are otherwise similar, what will be the relative fre- 
quencies ? 

10. One wire is 60 cm. long and stretched with 40 kg., and 
another similar one is 15 cm. long and stretched with 10 kg. 
What are the relative frequencies ? 

11. If the overtones of a wire are caused by its vibrating in 
three equal segments, what would be the frequency of the 
fundamental compared with the overtones ? 



SECTION 4. SOUND VIBRATIONS 

461. Sonorous Vibrations. — We may speak of the vibra- 
tions of sonorous bodies which are capable of producing 
sound-waves as sonorous vibrations. These may be the 
vibrations of some solid, or of the air itself ; but the 
necessary condition in either case is that the area of 
vibrating surface shall be large. 



§§ 462-4G5] SOUXB VIBRATIONS 291 

462. Sounding-boards. — ■ With all ordinary stringed in- 
struments the sonorous vibrations are those of the sound- 
ing-board and not of the strings. The area of the string 
is too small to set up effective sound-waves in the air, as 
the air so easily passes around the string. But the string 
sets up vibrations in the sounding-board, and this in turn 
imparts the vibrations to the air. So the sonorous vibra- 
tions are those of the sounding-board. 

463. Vibrating Air Columns. — In case of many other 
musical instruments, such as organ pipes, instead of a 
sounding-board the sonorous vibrations are those of a 
column of air the area of which is sufficient to set up effec- 
tive air vibrations. These air-column vibrations are set 
up either by the vibrations of some small solid as the 
tongue of a reed-pipe, or by the vibrations of small masses 
of air, as in the case of flutes or any flue pipes. To 
consider this, we should first consider sympathetic vibra- 
tions. 

464. Sympathetic Vibrations. — In order to start a child 
swinging in a swing it is necessary only to give the 
swing a slight push every time it comes back ; if the 
pushes are given just at the right time, one slight push 
for each complete vibration of the swing will increase 
rapidly the amplitude of vibration. This may be spoken 
of as sympathetic vibrations, — the swing vibrates in sym- 
pathy with the pushes. Similarly, heavy bells are rung 
by pulling the rope each time the bell swings back to the 
proper place. 

465. Resonance. — Strictly speaking, however, sympa- 
thetic vibrations are vibrations of one mass caused by the 
regular vibrations of some other mass. Such a case 
would be the vibrations of air columns mentioned above, 
and the increased sound produced by such a phenomenon 
is called resonance. 




292 SOUND [§§ 465-467 

Perhaps the simplest case of resonance is a vibrating 
tuning-fork held over the mouth of a tall jar or tube partly 
filled with water, as shown in Fig. 179. As the prong of 
the fork goes down, it gives to the air in the 
jar a push, causing a condensation ; this con- 
densation passes downward, strikes the water, 
and bounds back. If the water is the right 
distance from the fork, the condensation will 
reach the prong just as it is passing upward; 
that is, the condensation will travel down to 
the water and back to the prong while the prong* 

Fig. 179. i o jt o 

is making one-half a vibration. The conden- 
sation Avill then be driven down again by the surrounding 
air, with the assistance of the fork ; and thus the air 
column in the tube will vibrate up and down in sympathy 
with the fork. 

As the upper end of the air column is so much larger 
than the prong of the fork, it will greatly assist the fork in 
producing sound-waves in the air ; and the increased sound 
thus produced is resonance from sympathetic vibrations of 
the air column. 

466. Length of the Air Column. — Evidently, if the con- 
densation of the air column travels from the fork to the 
water and back while the fork is making one-half a vibra- 
tion, the length of the column from the fork to the water 
must be one-fourth the wave-length of the sound-wave 
produced by the fork. So if the frequency of the fork 
is known, the length of the wave can at once be deter- 
mined. 

Experiment shows, however, that the length of the col- 
umn depends somewhat on the diameter of the tube ; as 
the diameter increases, the column decreases. ■ 

467. Reed-pipes. — In case of reed-pipes, the tongue a 
(Fig. 180) is caused to vibrate by blowing through the 



§§ 4G7-469] 



SOUND VlBBATIONti 



293 



Fig. 180. 



mouth of the pipe, and the tongue m turn sets up sympa 
thetic vibrations of the air column in the tube 5, the vibra- 
tions of the air column being the principal factor 
in setting up sound-waves. 

468. The Human Voice. — The organs of the 
voice are similar in principle to the reed pipe, 
the vocal cords and the pharynx taking the places, 
respectively, of the tongue and the tube of the 
pipe. The vocal cords are two membranes extend- 
ing across the upper end of the larynx, separating 
it from the pharynx. The membranes lie in the 

same plane, and their free edges 
nearly meet across the center 
of the larynx, as shown in Fig. 181. 
The expired air from the lungs passing 
through the larynx and the slit formed 
b}^ the vocal cords, causes the cords to 
vibrate ; this in turn causes the air 
column in the pharynx to vibrate in 
sympathy, and audible vibrations are produced. By volun- 
tarily regulating the tension and position of the cords, 
various tones are produced. The shape of the pharynx 
and of the mouth may also be changed voluntarily, thus 
affecting the tones produced. 

469. Flue-pipes. — In case of pipes, which 
are called flue-pipes^ the tongue is replaced 
by a fixed lip a, Fig. 182. As the air is blown 
across the lip of the pipe, a portion of the air 
is caused to vibrate in and out of the opening, 
and this causes sympathetic vibrations of the 
air column in the tube. This is the arrange- 
ment of the ordinary church-organ pipes. 
Another familiar pipe of this character is the 
flute. 




Fig. 181. 




294 SOUND [§§ 470-471 

470. Sound-wave Vibrations. — Let us next consider the 
effect of these sonorous vibrations of sounding-boards and 
air columns upon the air which transmits the effect of tlie 
vibrations to the ear. 

When a sonorous body sets up sound-waves, it is the 
wave that moves outwardly and not the air. The air 
particles simply vibrate back and forth parallel with the 
direction the wave is travelling, and as a large number of 
particles act in unison, we may consider the entire motion 
, , of the air to consist of longitudinal 

► #ifi||'f#!'# vibrations of masses of air. Figure 
'' ^ « ^ 183 reprjesents the sound-wave pass- 

^^" ■ ing away from a tuning-fork. Con- 

sidering the dark portion to be the condensation of the 
wave, and the light portion the rarefaction, we may con- 
sider the mass a to be vibrating back and forth between 
the lines b and <?, and the mass d to be vibrating between 
e and g, the two masses colliding and rebounding at c. 

471. Graphic Representation of Waves. — Every one is 
familiar with the appearance of a water-wave as it passes 
outward from some point where a stone has been dropped 
into the water. There is a crest of water followed by a 
depression or trough. The surface of the water, if we 
consider only a cross- _ ^ 
section of the circular Vy ^ 
wave, would be as ^^" 

indicated in Fig. 184, the stone having been dropped at 0. 
So we represent graphically the wave travelling in one 
direction by a curved line, such as ah or cd. If the stone 
or a stick were caused to vibrate continually across the 
surface of the water, a wave would be sent out each 
time the surface of the water was disturbed ; and the series 
or train of waves thus caused might be graphically repre- 
sented as in Fig. 185. 



§§ 471-474] SOUND VIBRATIONS 295 

In case of sound-waves the particles vibrate parallel 
with the direction in which the wave is moving, instead of 
perpendicular to it. Yet, we may consider the condensed 
portion of the air similar to 
the w^ater crest, and the rare ^ \ ^\ \ 

portion similar to the trouofh, 

^ - , ° Fig. 185. 

and may then represent the 

wave graphically in the same manner. Thus, instead of as 
in Fig. 183, it is much more convenient to represent the 
sound-wave as in Fig. 185, and consider a dense portion at 
a^ a rare portion at 5, and a complete vibration between 
the points b and c, just as before. 

472. Fundamental Wave. — The wave represented in 
Fig. 185 is a simple wave, and may be considered as the 
wave sent out by the fundamental vibration of the sonorous 
body. We may therefore speak of it as the fundamental 
wave. 

473. Partial Waves. — As we have already seen, the 
fundamental vibration is always accompanied by partial 
vibrations ; and each of these vibrations necessarily sets 
up its own particular disturbance in the air, and forms, 
therefore, an independent wave, corresponding to its own 
frequency and amplitude. These waves may be called the 
partial waves. 

474. Coincident Waves. — Necessarily the fundamental 
and the partial waves, being given out simultaneously by 
the same sonorous body, must coincide with each other. 
They are therefore called coincident waves. In case of a 
vibrating string, for instance, while it vibrates as a whole, 
each half of the string vibrates at the same time. As the 
two halves send out waves of the same length, and as they 
start from practically the same place, we may consider 
them as coincident throughout, and may represent both by 
the same curved line. These waves, however, will be half 



296 SOUND [§§ 474-475 

as long as the fundamental, and we may represent the 
fundamental and the partial waves as in Fig. 186, the 

a dotted lines indicating the partial 

/^-s^^S^^^-y/^^^^\:^^.y waves. 

^' There are usually many other 

partial waves formed besides those 
of the two halves of the string. And it is not necessary, 
in order to have coincident waves, that they shall be 
formed by the same sonorous body. One body may be 
behind another ; as the waves go out in every direction, 
there will always be one set which will strike the other 
body, and will then coincide with its waves. Or two 
or more bodies side by side, like the wires of a piano or 
the pipes of an organ, will send out independent waves, 
which will strike the ear coincidently. 

475. Resultant Wave. — In all such cases there will 
evidently be a resultant effect on the air, and also on the 
ear. Hence a resultant wave will be produced by the com- 
bination of the independent waves. Referring to Fig. 186, 
at the left of a the two waves act together in condensing 
the air, and the condensation produced must be equal to 
the sum of the condensations produced by each. At h 
they act oppositely, and the resultant must be the differ- 
ence between the separate effects ; and so on. Hence, 
speaking of the rarefactions as minus condensations, we 
may say, the resultant wave is the 
sum of the two waves ; and we may 
represent it as in Fig. 187. 

Similarly, there might be a result- 
ant formed by the fundamental and all its partials, or 
with two or more waves from different sonorous bodies ; 
but such resultants are too complex to be considered in 
this discussion. So we will consider only one other case, 
and that is the production of beats. 



§§476-477] SOUND VIBRATIONS 297 

476. Beats. — If two consecutive notes of a piano are 
sounded simultaneously, especially two of the lower notes, 
the combined sound will rise and fall in intensity several 
times a second; there will be noticeable what may be called 
swells in the sound, or, as they are called in physics, beats. 
These beats are of great importance in music, and it will 
be well to discuss the cause. 

Let us consider, for simplicity, only the fundamental 
waves. Suppose w^e have two coincident trains of waves, 
the waves of one train 

slightly longer than jXfmCIJfMMXP 
those of the other. We 

rIG. loo. 

may represent the two 

trains as in Fig. 188, and the resultant will be as shown 

in Fig. 189. 

Evidently, where the condensations and the rarefactions 

of the two waves nearly coincide, the sounds will be more 

f\ f\ A A A i^^®^^®' because the re- 

A. /.\ Ay^ sultant amiDlitude will 

\J \y ^ ^ V \y be much greater, as 

^'''- ^^^- shown in Fig. 189 ; 

while where the condensations and the rarefactions oppose 

each other, the sound will nearly die out. This resultant 

increase and decrease in intensity is what causes the rise 

and fall in the sound as heard, or the so-called beats. 

477. Frequency of Beats. — A few trials with different 
notes of the piano will show that 'audible beats are pro- 
duced in only a few cases ; and careful experiments, as 
well as theory, shows that, in some cases, the beats are too 
frequent to be audible, in others they do not exist at all. 
Evidently there will be no beats if one wave is twice the 
length of the other, because the coincidence of condensa- 
tions and rarefactions will be the same for each of the 
longer waves as for every other — the shorter wave will 



298 SOUND [§ 477 

gain a full wave-length for each wave-length of the longer. 
For the same reason there will be no beats if one wave- 
length is any simple multiple of the other. 

If, however, such a simple relation does not hold, there 
will be beats, and the number per second will depend on 
the difference in frequency of the two vibrations produc- 
ing the waves. If one frequency is 200 and the other 201, 
the shorter wave will gain one length per second on the 
other and there will be one beat per second. And so in 
every case the frequency of beats equals the differences in 
frequencies of the vibrations. 

The frequency of beats plays an important part in 
music, as we shall see, and aids very much in tuning 
musical instruments ; because so long as beats are percep- 
tible, the notes sounded are not of the same pitch, and 
hence not in tune. 

EXERCISES 

1. Neglecting the effect of the diameter of the tube, what 
will be the distance of a tuning-fork above the water in a tube, 
if resonance is produced and the frequency of the fork is 256, 
when the temperature is 0°? 

2. What will be the frequency of the fork if the distance 
to the water is .5 m. ? 

3. What will be the speed of the sound if the frequency is 
280 and the distance is .3 m. ? 

4. Represent graphically two coincident trains of sound- 
waves, the length of the waves of one being three times that 
of the other. 

5. Represent the resultant of two trains, the waves of one 
being four times as long as the other. 

6. What will be the frequency of the beats between two 
wires, the frequencies of which are respectively 280 and 291 ? 
363 and 490 ? 236 and 572 ? 

7. If 4 beats per second are heard, and the frequency of one 
vibration is 218, what may be the frequency of the other ? 



§§478-479] BECEPTION OF SOUND-WAVES 299 

SECTION 5. RECEPTION OF SOUND-WAVES 

We have now to consider the effect of sound-waves 
upon various apparatus, such as the phonograph, the tele- 
phone, and particularly the ear. We wish to see how the 
waves are received by such apparatus. 

478. Forced Vibrations. — If the damper of a piano is 
raised, so the wires may vibrate freely, and a note is then 
sung into the piano, the wire which is in unison with the 
note will begin to vibrate, and will give back the same 
note when the singing has ceased. The wire vibrates in 
sympathy with the vocal cords because of the impulses it 
receives from the sound-waves. Similarly, a membrane 
stretched over a ring, like a drumhead, will be caused to 
vibrate by sound-waves striking it. But, the membrane 
will be forced to vibrate whether or not it is in unison 
with the sound-wave; and it will be forced to vibrate 
with a frequency equal to that of the sonorous body. 
Such a vibration is called a forced vibration. 

A drumhead is too rigid to be much affected by ordi- 
nary sound-waves ; but a properly arranged membrane or 
disk will vibrate in unison with any sound-wave that may 
strike upon its surface. And this is the principle involved 
in all arrangements for the reception of sound-waves. 

479. The Ear. — The external ear appears to have little, 
if any, influence on the sense of hearing ; its only value, 
perhaps, is to assist in determining the direction from 
which the sound-waves come. 

The auditory canal, which connects the external with 
the internal ear, serves to direct the sound-waves against 
the drum, or tympanic membrane, of the ear. 

The tympanic membrane is acted upon by the waves, 
and is forced to vibrate in unison with every sound-wave 
which strikes it. 



300 SOUND [§§479-480 

By means of a small bone, called the hammer, attached 
to the tympanic membrane, the vibrations of the mem- 
brane are passed along through the inner ear to a set of 
several thousand fibers of different lengths. 

It is supposed that sympathetic vibrations are set up in 
these fibers by the vibrations transmitted through the ear 
to them, each fiber responding to a certain pitch or fre- 
quency just as each piano wire will respond to a certain 
note sung into the piano. 

The energy which is thus imparted to these fibers is, in 
some way, transmitted along the auditory nerve to the 
brain, which in turn, in some unknown way, interprets the 
effects into sound. 

This is but a ver}^ general description of the ear ; there 
are many interesting details that would be out of place 
here ; but it is sufficient to give some idea of the marvellous 
nature of the ear, and to show how strictly it carries out 
the ordinary laws of physics. 

480. The Phonograph. — In 1878 Thomas A. Edison 
invented the phonograph. This is an apparatus which 
not only receives and records the effects of sound-waves, 
but also gives the waves back again to the air, when 
required, with little change in form from the original 
waves. So, then, if a person speaks into the phonograph 
it may afterward be made to repeat the same sounds. 

So far as receiving the waves is concerned, the phono- 
graph is very similar to the ear. The sound-waves are 
directed into a funnel-shaped tube, which collects the 
waves and directs them against a diaphragm. The dia- 
phragm takes the part of the tympanic membrane of the 
ear ; it is forced to vibrate in unison with the impinging 
waves. This causes to vibrate a sharp-pointed stylus 
which is attached to the center of the diaphragm, just as 
the hammer bone is vibrated by the ear membrane. The 



§480] RECEPTION OF SOUND-WAVES 301 

stylus penetrates slightly into the surface of a cylinder or 
a disk of wax. The cylinder is caused to rotate by some 
external force and at the same time is moved forward 
gradually on its axis. If now a sound-wave strikes the 
diaphragm, the stylus, while vibrating, will gouge out a 
continuous channel in the moving wax surface, and the 
bottom of the cliannel will form a wave curve similar to 
the graphic representation of the sound-ivave which strikes 
the diaphragm. The channel will wind spirally around the 
cylinder from end to end. So a complete record of the 
sound-wave is thus made. 

To make the apparatus give back the sound-waves and 
"talk," it is necessary only to pass the stylus with the 
diaphragm attached over the record on the wax, rotating 
the cylinder and moving it forward just as before. As 
the stylus rises and sinks along the curve at the bottom 
of the channel, it will cause the diaphragm to vibrate just 
as it did when affected by the original sound-waves, and it 
will thus become a sonorous body and will set up sound- 
waves of the same character as the original. 

It is interesting to notice that if the cylinder is rotating 
when the apparatus is " talking " at the same rate as it 
was when it was receiving the sound, the pitch of the sound 
in the two cases will be the same. But the pitch when 
" talking " will be higher or lower than the original if the 
rate of rotation is higher or lower than the original. This 
follows as a matter of course from the fact that pitch 
depends upon the frequency. 

Phonographs have become of value in the business world 
and are also the cause of much desirable amusement. But 
if a receiving apparatus could be invented that would 
register the sounds on paper so that the record would be 
as legible as ordinary handAvriting, it would be one of the 
most valuable inventions ever produced. And with the 



302 SOUND [§§480-483 

phonograph, telephone, and other apparatus as guides, such 
an invention appears much more possible than did the 
phonograph thirty years ago. 

481. The Telephone. — The function of the phonograph 
is to produce sounds at some future time, — to extend 
sound in time ; while the function of the telephone is to 
produce sounds at some distant place, — to extend sound 
in space. There are two classes of telephones, the acoustic 
and the electric telephone. 

482. The Acoustic Telephone. — Suppose a phonograph 
diaphragm has attached to its center the end of a wire in- 
stead of a stylus, and the wire is drawn taut. When 
sound-waves impinge upon the diaphragm, causing it to 
vibrate, the tightness of the wire will be alternately in- 
creased and decreased ; 
it will, in fact, be made 
to vibrate longitudinally 

Fig. 190. "-^ . . .° . ,. -^ 

m unison with the dia- 
phragm. Now, if the other end of the wire is attached 
to the center of another similar diaphragm, as indicated in 
Fig. 190, this diaphragm will also be caused by the wire 
to vibrate in unison with the first diaphragm, and will give 
out sound-waves of the same nature as the original waves. 
This is the general principle of the acoustic telephone. 
The first diaphragm, with its appurtenances, is called the 
transmitter, while the second is called the receiver. The 
two, however, are interchangeable, and may be just alike, 
so that a person may talk into either one. If properl}^ 
arranged, sound may be very distinctly transmitted many 
hundred feet with this telephone. 

483. The Electric Telephone. — The telephone in general 
use to-day required about twenty- five years for its devel- 
opment, and it is the work of many minds. It was first 
conceived in 1854 by Charles Bourseul of France. The 



§§ 483-484] MUSIC 303 

first attempt to apply the conception to a suitable appa- 
ratus was made in 1860, by Philip Reis of Germany. In 
1876 the first practical telephone was patented by Bell, 
and a jesiV or two later the instrument was brought to 
about its present state of perfection by the assistance of 
Edison and Hughes. 

Articles 411 and 412 give a description of the telephone 
in its present form so far as electricity is involved. It 
remains now only to show the application of the principles 
of sound. When a sound-wave impinges upon tlie dia- 
phragm of the transmitter of the telephone system, the 
impacts of the sound-waves cause forced vibrations of the 
diaphragm, and the diaphragm responds so sensitively to 
the sound-waves that practically every partial, as well as 
every fundamental, vibration of the wave is effective ; so 
the segments of the diaphragm vibrate in unison with the 
segments of the sonorous body. Each fundamental and 
each partial vibration produces its proper effect on the 
current flowing from the transmitter to the receiver, and 
every change in the current produces its proper effect on 
the diaphragm of the receiver, causing fundamental and 
partial vibrations of the diaphragm exactly corresponding 
to those of the transmitter diaphragm and also of the 
sonorous body. So the diaphragm of the receiver acts as 
a sonorous body setting up sound-waves very similar to 
those originally set up by the organs of the voice. 

SECTION 6. MUSIC 

484. Simple Sounds. — When a single sound-wave 
strikes the ear, the effect is a simple sound. A single fun- 
damental vibration of a sonorous body will set up a single 
wave and thus produce a simple sound. But it is seldom 
if at all that such a phenomenon occurs ; most sounds are 



304 SOUND [§§ 484-492 

complex, being the result of innumerable waves of various 
descriptions. 

485. Simple Tones. — A train of similar waves striking 
the ear produces a tone. If the waves are simple, — that is, 
the result of fundamental vibration only, — the tone is a 
simple tone. Hence, a fundamental tone alone is a simple 
tone ; but it is doubtful if there are any, — perhaps the 
nearest approach is that of the tone of an ordinary tuning- 
fork. 

486. Complex Tones. — A complex tone results when 
there is a combination of a fundamental Avith its overtones. 
Such tone is the usual result of the vibrations of almost 
any body. 

487. Noise. — An irregular combination of sounds and 
tones is called a noise, such as the rattling of a wagon over 
a stony road. It may be spoken of as a combination of 
sounds that cannot be readily resolved into simple tones. 

488. Music. — Music results from such a combination 
of tones as is pleasing to the ear, and may be resolved 
into its simple tones. The elementary principles of music 
are simple and may be profitably considered here. 

489. Consonance. — When two or more tones not in uni- 
son are sounded together, and a pleasant sound results, the 
notes are consonant and the result is harmony or consonance, 

490. Dissonance. — If, in such case, a disagreeable sound 
results, a harsh grating sound, the tones are dissonant, and 
the result is discord or dissonance, 

491. Cause of Dissonance. — Dissonance is due largely 
to beats between some of the tones. The beats may be 
between the fundamental tones or between the overtones, 
or between the fundamental and the overtones. 

492. Harmonics. — An overtone results when any por- 
tion, or segment, of a vibrating body vibrates by itself. 
Ordinarily such segment, especially with a vibrating string, 



§§492-495] MUSIC " 305 

is one-half, one-third, or some aliquot part of the string. 
And in such case no beats are formed between the funda- 
mental and the overtone, as explained in Art. 477. Hence, 
such overtone is always in harmony or consonance with its 
fundamental, and it is called, for this reason, a harmonic. 

493. Musical Interval. — The foregoing discussion brings 
us ta one of the elementary principles of musical vibra- 
tions. In the first j)lace, a musical interval is the ratio 
between the frequencies of the tones producing the com- 
plex tone. If the frequency of one tone — that is of the 
vibration producing it — is twice that of the other, the 
ratio, or musical interval, is two. And the principle is 
that the musical interval should be as simjjle as possible ; it 
should be some small number, or simple fraction. 

494. The Octave. — The simplest ratio or musical inter- 
val is 2 : 1, or 2. This interval is called the octave. Thus, 
when one string vibrates twice as fast as another, its tone 
is the octave of that of the other. The interval 3 gives one 
tone tAVO octaves higher than another, and so on. This is 
exactly the case with vibrating strings or wires ; the first 
partial vibration is one octave above the fundamental, the 
second two octaves above the fundamental, and so on. 
Thus, middle C on the piano has about 264 vibrations per 
second, so its first harmonic would have 528 vibrations. 

This interval is called the octave from octavus^ the Latin 
for eighth, as it is the interval between the eighth note 
on the musical scale (Art. 498) and the first note. 

495. The Fifth. — The next simplest interval would be 
3 ; 2, or |, the higher note gaining on the lower one vibra- 
tion while the lower vibrates twice. This interval is 
called the fifths and it is next to the octave in respect 
to consonance. As | of 264 is 396, the fifth of middle C 
would have 396 vibrations. This is the interval between 
the first note on the scale and the fifth note. 



306 SOUND [§§496-498 

496. The Fourth and Third. — The next simpler com- 
bination is the interval 4:3, or |. This is called the 
fourth. The next is | and is called the third. These are 
the respective intervals between the first and the fourth 
and the first and the third notes on the scale. 

497. Chords and Triads. — Several harmonious tones 
sounded together form a chords and a chord consisting of 
a note sounded in combination with its fifth and third is 
called a triad. 

498. Musical Scale. — A musical scale is a graduated 
series of tones consisting usually of eight notes. The 
lowest tone is called the key-note ; the highest is the 
octave of the key-note ; and the remainder are inter- 
mediate tones, including the fifth, fourth, and third. 

The major scale has C for its key-note, and the other 
notes are named respectively D, E, F, G, A2, B2, Cg. They 
are also called by the syllables do^ re, mi, fa, sol, la, ti, do. 
The following table gives the absolute frequencies of the 
tones of the major scale, having middle C, with a frequency 
of 256, for its key-note, and also the relative frequencies, 
or intervals. 



c 


D 


E 


F 


G 


A, 


B, 


C.o 


do 


re 


mi 


fa 


sol 


la 


ti 


do 


256 


288 


320 


341.3 


384 


426.6 


480 


512 


1 


1 


i 


t 


f 


1 


¥ 


2 



These are the vibrations usuallv followed by physicists ; 
but musicians have adopted a slightly higher pitch. It 
will be seen that G is the fifth of C, and E is its third. So 
these form a major triad. The relative frequencies of 
these tones are 4:5:6. The remainder of the major scale 
is composed of two other major triads, the relative fre- 
quencies of which are similarly 4:5:6. One of these triads 
is F, Ag, and Cg, and the other G, Bg, and D2, or D. 



§§499-500] MUSIC 307 

499. Notes. — A note is a tone of definite length. Music 
depends not only on a proper combination of tones, but 
also on tones of proper lengths. 

500. Musical Notation. — The length and pitch of notes 
are indicated by the form and position of certain char- 
acters, as indicated in Fig. 191. The form of C indicates 
what is called a whole note ; D is a half-note, its length 



^ — ^ 



^j)^ I J J J ^ ^ 



- 'T D E F G Aj, B2 Cj Dg E^ F^ G^ 

Fig. 191. 

being half that of C ; E is a quarter-note, being one-fourth 
as long as C ; F is an eighth-note, one-eighth of C ; G is a 
sixteenth, and A^ is a thirty-second, while B2 and C^ are 
sixty-fourth notes. The position of the note with refer- 
ence to horizontal lines or bars determines its frequency. 

EXERCISES 

1. What is the interval between the first and the second 
harmonic of middle C ? 

2. If the frequency of a tone is 236, what is that of its 
octave ? its fifth ? its third ? 

3. What is the relative frequency of the two higher tones in 
a major triad ? 

4. A violin string 18 inches long sounds a certain tone. 
How much must it be shortened to sound the fifth of that 
tone? the third? 

5. What must be the relative lengths of a violin string in 
order to sound successively C, D, E, F, Ao, B2, and C2 ? 



CHAPTER IX 

LIGHT 

SECTION 1. NATURE OF LIGHT 

501. Source of Light. — The sun is by far our greatest 
source of light. Other natural sources are the moon and 
stars. As artificial sources we have various burning sub- 
stances, and white-hot substances such as incandescent 
lights. 

502. Self-luminous Bodies. — The carbon of the electric 
lamp is heated intensely hot by the electric current, and 
thus gives off light. And it may be noticed that all bodies, 
when heated very hot, give off light as well as heat. All 
such bodies are called self-luminous bodies^ because they 
are the original sources of the luminous effects which we 
call light. All burning substances are self-luminous. 

503. Non-luminous Bodies. — Ordinarily the walls of a 
room, and the various articles in the room, give off more 
or less light — they appear to be self-luminous. But if 
the shutters of the room are tightly closed, and all arti- 
ficial lights are excluded, the room and its contents become 
perfectly dark; they are evidently not at all luminous. 
All such bodies are non-luminous. They appear luminous 
ordinarily, because the light from some self-luminous body 
is reflected from them to the eye. 

504. Nature of Light. — All bodies, sufficiently heated, 
give out light, and most self-luminous bodies are hot. It 
is true, there are a few bodies, such as phosphorescent 
substances, that give out light without heat. But it is 

308 



§§501-507] NATURE OF LIGHT 309 

evident that heat and light are very closely related; it 
is undoubtedly true that they are of the same nature, 
differing only in degree ; while heat is caused by the 
slower vibrations of the molecules of which the substance 
is composed, light is caused by the more rapid vibrations. 
Light, then, is simply the effect of sufQciently rapid 
vibrations of molecules. As we found out under Heat, 
vibrating molecules set up disturbances in the surround- 
ing ether ; these disturbances move outward through the 
ether in every direction, and if the vibrations are suf- 
ficiently rapid, the disturbance will be able to affect the 
retina of the eye and cause sight. Such a complete phe- 
nomenon is called light. But, as with sound, we may 
divide the phenomenon into three factors : the body caus- 
ing the light, the passage of the effect through space, and 
the effect on the eye. Just as we have sonorous bodies, 
sound-waves, and hearing, so we have self-luminous bodies, 
light-waves, and vision. 

505. Energy of Self-luminous Bodies. — Evidently as 
light is due to the vibrating motion of molecules, it is due 
to their kinetic energy. When the kinetic energy of the 
vibrations of the molecules becomes sufficiently great, the 
body becomes self-luminous. And this light energy, just 
as heat energy, is imparted to the surrounding ether. 

506. Radiant Energy of Light. — The light energy im- 
parted by the rapidly vibrating molecules to the ether 
travels outward through the ether. Thus the energy of 
light is radiated through space, just as is the energy of 
heat ; and to distinguish between the two forms we may 
speak of radiant energy of heat and of lights or simply heat 
and light. 

507. Vision. — The third factor involved in the phe- 
nomenon of light is sight or vision. - Just as the energy 
propagated through the air from the sonorous body affects 



310 LIGHT [§§ 507-510 

the ear and causes hearing, so the energy of the luminous 
body travels through the ether and affects the eye, pro- 
ducing vision. This will be considered more fully here- 
after. 

SECTION 2, PROPAGATION AND TRANSMISSION OF 

LIGHT 

508. Manner of Propagation. — As already suggested, 
the energy of luminous bodies is propagated through 
space by the ether. The manner of propagation is 
very similar to that of sound. The vibrating molecules 
of the luminous body set up disturbances in the ether 
which travel outward in every direction in the form of 
a constantly enlarging train of spherical waves. 

509. Light-waves. — The light-weaves thus set up differ 
from sound-waves in three important particulars: First, 
they are composed of vibrating portions of the ether 
instead of vibrating masses of molecules. Second, the 
vibrations, as we shall see later, are far more rajnd than 
those of sound-waves. And third, the vibrations are 
transverse instead of longitudinal. 

We may represent light-waves graphically, however, 
exactly as we have sound-waves. In fact, a transverse 
wave is more literally represented by the graphic curve, 
because the vibrations, just as water-waves, are across 
the line of travel. In many other respects we shall find a 
very close analogy between light-waves and sound-waves. 

510. Light-waves and Heat-waves. — There is, however, 
between light-waves and heat-waves a much closer simi- 
larity than between light- waves and sound-waves. In 
fact, the only difference, apparently, between them is that 
the average light-waves are somewhat shorter than the 
average heat-waves. This is because the frequency of 
vibration causing the light-waves is usually greater than 



§§ 510-513] PROPAGATION OF LIGHT 311 

that causing the heat-waves. Yet the same frequency often 
causes both waves. 

511. Direction of Propagation. — Light-waves are propa- 
gated by the ether, unless interfered with, in every direc- 
tion from the source and in perfectly straight lines. That 
they are propagated in every direction is evident at once 
when we consider that any luminous body may be seen 
from any surrounding point, providing nothing interferes. 
And that they are propagated in straight lines may be 
shown by placing a screen in a straight line from the eye 
to the luminous body, for the luminous body at once 
disappears. Or it may be shown better, perhaps, by look- 
ing at an object through a long, straight tube ; if the tube 
is then bent slightly, or if it is replaced by a bent one, the 
object can no longer be seen. Of course, in any such 
experiments one eye should be closed; and it should 
also be remembered that any object is seen only because 
light is passing from it to the eye. 

512. Opaque Bodies. — When a body, such as a piece of 
cardboard, is held between the source of light and the eye, 
the light disappears ; the board seems to interfere with the 
waves of light to such an extent as to cause them to be 
entirely destroyed. We may say the ether cannot propa- 
gate the waves through the board, or, that the board will 
not transmit the waves. Bodies that act in this manner 
are called opaque. 

513. Translucent Bodies. — If, however, the paper used 
is very thin, like tissue paper, or especiall}^ if it is greased, 
and the light is bright, some of the light seems to be trans- 
mitted by the paper. The form of the luminous body 
may be very indistinct ; but that it is luminous shows 
plainly through the paper. Bodies such as plates of ground 
glass, which thus transmit some light but not enough to 
show the form of the luminous body, are called translucent. 



312 LIGHT [§§ 514-515 

514. Transparent Bodies. — Other bodies, such as pieces 
of window glass, seem to transmit light without any inter- 
ference with the waves. The form of the luminous body, 
as well as its light, are clearly discernible. Such bodies 
are called transparent. 

It should be borne in mind, however, that we cannot 
class substances as either transparent, translucent, or 
opaque. Clear water, when not too deep, seems perfectly 
transparent ; but if deep enough, it is entirely opaque. A 
film of silver may be deposited on glass so thinly as to 
interfere scarcely at all with the transparency, or it may 
be so thickly deposited as to be perfectly opaque. Gold- 
leaf, which is ordinarily opaque, or at least translucent, 
may be made so thin as to be transparent. So it is evi- 
dent that the same substance may be transparent, trans- 
lucent, or opaque ; and it is also evident that there is no 
strict line of demarcation between transparency and trans- 
lucenc3% or between translucency and opaqueness. 

Thus it is throughout the physical world : depending 
on its surroundings and its condition, a substance may be 
transparent, translucent, or opaque ; it may be a solid, a 
liquid, or a gas ; it may be hard or soft, brittle or plastic, 
hot or cold, light or heavy, dense or rare ; it may be a good 
or a poor conductor of heat or electricity. And so it is that 
we must classify substances, not ahsolutely but relatively ; 
we must class them Avith reference to their conditions or 
surroundings, and with relation to some standard. 

515. Shadows. — Everybod}^ is familiar with the shad- 
ows formed when an opaque screen is brought between a 
wall or other body and a luminous body. In such case 
the waves striking the screen are destroyed — the energy 
is used in agitating the molecules of the screen. Hence, 
as light travels in straight lines, the wall opposite the 
screen is not illuminated. 



§§ 515-517] 



PBOPAGATION OF LIGHT 



313 




In Fig. 192, L represents a luminous point of light, S a 
screen, and C the shadow. In such case we have, accord- 
ing to geometry, BO: AS = 
CL : SL. We have, then, 
the ratio between the leiigths 
of the shadow and of the 
screen equal to the ratio 
between their respective distances from the luminous point. 

516. Umbra and Penumbra. — If, however, the luminous 
body is large, such as the flat side of an ordinary gas or 
lamp light, the relation between the screen and the 
shadow is not so simple. The simple relation mentioned 
above holds between the screen and the shadow formed 
by any poiyit of the luminous body ; but as the shadows 
from all the points overlap^ the entire shadow formed by 
all the points of the light is complicated. 

In Fig. 193, the light from a fails to strike the wall 
between a' and a" \ that from h fails to strike between h' 
and h" . Similarly, it may be seen that no light whatever 

falls between h' and a\ 

-^^ --^—r \\ /iMK - ^^^ ^^^^ more and more 

■fc'"' 




light falls outside the 
circle V a^ until the circle 
a^^V^ is reached, wdien all 
the light from every point reaches the wall. Within 
Va\ then, there is a uniform dark shadow. This is 
called the umbra. Without V a^ the shadow becomes 
gradually less dark until a^^V^ is reached. This portion 
is called the penumbra. 

517. Intensity. — Intensity of light, as with sound, is 
the amount of energy it contains — the amount of energy 
given out by the luminous body, or transmitted by the 
ether, or affecting the eye. The effect of the intensity on 
the eye is spoken of as the brightness ; this, however, like 



314 LIGHT [§§ 517-519 

loudness of sound, depends on the condition of the organ — 
the eye or ear ; it is intensity physiologically considered. 
The intensity of a light is measured by comparing its 
brightness with that of some standard light. To find the 
specific gravity of any substance, we find how many times 
heavier it is than a like volume of the standard substance, 
water ; and similarly, to find the intensity of a light, we 
find how many times brighter it appears than some stand- 
ard light. The standard is a sperm candle burning 120 
grains an hour, and such a light is spoken of as one candle- 
power. 

518. Photometry is the measurement of light intensity 
under various conditions. There are two cases of general 
interest, one the determination of the effect of distance on 
the intensity of illumination of light, and the other the 
determination of the candle-power of lights. We will 
consider these briefly. 

519. Effect of Distance. — Every one is familiar with the 
fact that the light falling upon a surface becomes dimmer 
as the distance from the source becomes greater. Evi- 
dently, as with sound, the energy in a unit area of the 
surface of the expanding spherical wave becomes less as 
the distance increases. To determine the exact effect of 
distance, the following method may be employed: 

If a greased spot is produced in a screen of thin unsized 
paper, slight differences in illumination of the two sides of 
the paper will be indicated by differences in the appear- 
ance of the two sides of the spot, and when the sides 
appear alike the amount of illumination will be equal. 
Hence, if the room is darkened, and two similar candles 
are placed at equal distances on opposite sides of the 
screen, the spot will appear the same on the two sides. 
Then if one candle is removed twice as far away, it will be 
found that three more similar candles must be added to it 



§§ 519-521] PROPAGATION OF LIGHT , 315 

before the spot is again equally illuminated on the two 
sides. That is, if the source of light is twice as far away, 
it must be four times as intense to produce the same effect, 
or, if of the same intensity, its effect will be one-fourth as 
great. Similarly, it will be found that nine candles are 
required when they are three times as far away, or that 
the effect is one-ninth as great when the light is three 
times as far away. The apparatus thus used is called the 
Bunsen photometer. 

This shows that the intensity of illumination varies 
inversely as the square of the distance. The brightness 
with which the light itself appears to the eye, however, 
does not change with the distance, as the surface of the 
retina upon which the light is concentrated decreases at 
the same rate as the intensity of illumination. The light 
appears smaller as the distance increases, but, considering 
equal areas, it appears equally bright. 

520. Candle-power of Light. — To determine the candle- 
power of a light, a Bunsen photometer may be used, as 
follows : The light in question is placed one side of the 
screen, at such a distance as to illuminate the spot equally 
with a standard candle placed a convenient distance on 
the other side. Then, according to the law above, the 
square root of the ratio between the two distances will 
give the ratio between the two intensities ; and this ratio 
will be the candle-power sought-, as the candle-power of 
the standard is one. 

521. Speed of Light. — Various methods, some physical 
and some astronomical, have been used to determine the 
speed of light. The results differ somewhat, but the speed 
is evidently in the neighborhood of 300,000,000 m., or 
186,000 mi. per second. This is so great it is not strange 
that up to the seventeenth century light was supposed to 
travel instantaneously. Yet it travels so slowly that it 



316 , LIGHT [i 

requires many years to reach us from even the nearest 
stars. 

Probably the most accurate determination of the speed 
of light was made in 1883 by Professor Michelson. His 
results indicate the speed to be 299,853,000 m. 

522. Likeness of Heat and Light. — Experiments indi- 
cate that all of the foregoing facts in regard to light are 
equally true for heat. Unquestionably, at least, the fol- 
lowing facts are true : 

Heat-waves are propagated in straight lines. 

Some bodies are opaque to heat-waves, or are, as it 
is called, athermic ; while other bodies, which are called 
diatliermic, allow the weaves to pass freely through them. 

Radiant heat may be screened by the use of athermic 
bodies, just as light may be by using opaque bodies. 

The intensity of heat varies inversely as the square of 
the distance ; and there is much reason to believe that the 
speed of heat-waves is the same as that of light- waves. 

EXERCISES 

1. A round screen, 1 dm. in diameter, is placed between a 
light and a wall, 1 m. from the light and 3 m. from the wall. 
If the som-ce of light be a point, what will be the area of the 
shadow ? 

2. What would be the relative intensities of the light on the 
screen and on the wall ? 

3. How many times could the light travel to the wall and 
back in 1 sec. ? 

4. What must be the candle-power of a light 5 ft. away from 
a printed page to illuminate the page as much as a 6 candle- 
power lamp 18 in. from the page ? 

5. If the source of liglit in Exercise 1 was a white-hot ball 
10 cm. in diameter, what would be size of the umbra? of the 
penumbra ? 



§ 523] BEFLECTION OF LIGHT 317 

6. If the ball was 20 cm. in diameter, how far would it need 
to be removed from the screen to cause the umbra to disappear 
from the wall ? What then would be the size of the penumbra ? 

SECTION 3. REFLECTION OF LIGHT 

523. Reflection of Light. — When a. ball strikes against 
a wall, it bounds back ; and, as we have seen, it is the same 
with a sound-wave, — if it strikes a wall it bounds back. 
Instead of passing into the wall the sound wave is re- 
flected back into the medium through which it came. The 
molecules of the sound-wave, impinging on the surface of 
the wall, cause a pressure upon it ; the wall reacts on the 
molecules, and they are driven backward. It is just the 
same with light-waves ; the vibrating portions of ether, im- 
pinging upon a reflecting surface, cause a pressure upon the 
surface, and it in turn, reacting on the waves, causes them 
to bound back into the medium through which they came. 

Reflection of light, then, is the turning hack of light-waves, 
hy the substance upon which they strike, into the medium 
through which they came. Perhaps the most familiar ex- 
ample of this is the effect produced by the ordinary mirror 
or looking-glass ; the 
light passes from objects 
in the room to the mirror, 
and is reflected by the 
mirror into the eye. 

If a beam of sunlight 
is allowed to enter a 
darkened room through 
a hole in the shutter, as 
indicated in Fig. 194, the 
beam will be plainly visible, because of the dust particles 
in the room. And if it falls upon a mirror, as shown, 
the reflected ray may also be seen. 




Fig. 194. 



318 LIGHT [§§ 524-527 

524. Rays. — The word ray is used for convenience, 
to indicate the |?a^7i along which the front of any wave 
travels. It does not refer to any portion of the wave, but 
simply to the line of direction of any particular portion of 
the wave-front. The term is used mainly with reference 
to light- waves. The ray is always perpendicular to the 
wave-front. 

525. Incident and Reflected Rays. — Whenever a light- 
wave strikes upon any surface it may be called an incident 
wave, and any ray along which travels any portion of the 
wave which strikes the surface, is called an incident ray. 
Similarly, a reflected ray is any ray along which travels 
any portion of the reflected wave. Upon the same sur- 
face, and from the same luminous point, of course, there 
may be an infinite number of incident rays, as indicated in 
Fig. 195. 

526. Direction of Reflection. — Every child knows that 
the direction in which the ball bounds depends upon the 
direction in which it strikes the wall. If it strikes per- 
pendicularly it bounds right back perpendicularly, curving 
downward, however, because of gravity. If it strikes at 
an acute angle, it bounds aivay from the thrower, and at 
an acute angle with the wall. Similarly with light : the 
direction of the reflected ray depends upon the direction 
of the incident ray, and their relative directions follow a 
definite law, which Ave will noAV consider. 

527. Angles of Incidence and of Reflection. — Referring 
to Fig. 194, suppose AO to be an incident ray of light, 
BO to be the reflected ray, and CO a line perpendicular to 
the reflecting surface. Then ^.06* is called the angle of 
incidence, and BOO tlie angle of reflection. That is, the 
angle of incidence is formed by the incident ray and the 
normal to the reflecting surface, and the angle of reflection 
is formed by tlie reflected ray and the normal. 



§§ 528-530] BEFLECTION OF LIGHT 319 

528. Law of Reflection. — Many experiments show tliat 
whenever a ray of liglit falls upon any reflecting surface, 
the angle of incidence equals the angle of reflection. 

Care should be taken not to confuse the angles of in- 
cidence and of reflection with the angles formed by the 
rays and the reflecting surface. It is true the latter are 
necessarily equal if the former are equal ; but there are 
reasons, which we shall see hereafter, for taking AOQ and 
BO C ?is the angles of incidence and of reflection. 

Another portion of the law is that the two angles always 
lie in the same plane. So the full scope of the law is that, 
no matter how much AOO increases or decreases, BOO 
will increase or decrease accordingl}^, so the two angles 
will always be equal ; and the rays A and B 0, and the 
normal CO, will always lie in the same plane. 

529. Regular Reflection. — If the surface upon which the 
light-wave strikes is very smooth, as is the case with an 
ordinary mirror, the reflection 

will be regular; that is, all of 
the rays will bear just the same 
relation to each other after the 
reflection as they would if there \ ''\^ ^^^^ 

had been no reflection. Thus, \ \ ^^^-. , 

in Fig. 195, if i> is a point of . 

light and mm' a reflecting sur- 
face, the rays efy will diverge in just the same way as 
if they had travelled undisturbed to e'f'g'. This follows 
readily from the law of reflection. 

530. Images. — As a consequence of regular reflection, 
images are necessarily produced by mirrors whenever we 
have light from objects falling upon them. Whenever 
we look into a plane mirror we see behind the mirror 
images of the various neighboring objects. Such images 
are too common to need further discussion. But in order to 





320 LIGHT [§§ 530-531 

understand why we see images of objects behind mirrors, 
let us first consider why objects are seen at all. In Fig. 196 
let us suppose a luminous point to be at L. Rays of light 
diverge from the point, and travel in every direction ; 
the ray / enters the eye placed at E^ and the eye sees the 
point in the direction fL. Now, the 
only indication the eye has of any 
luminous point, so far as/ is concerned, 
is a ray entering it from a certain direc- 
tion. It is in no way otherwise affected 
by the point, or by the wave travelling 
in the ether between it and the point, 
so far as the ray/ is concerned. So, if there were but the 
one ray, it would be impossible to tell how far away the 
point was. But the ray g also enters the eye ; the eye also 
sees the point in the direction gL\ and necessarily the 
object appears to be at the point L where the two rays 
meet. There are, of course, an infinite number of other 
rays entering the eye, but as they all meet at the same 
pointy i, we need consider only two. 

If, now, we have a luminous body instead of a point, we 
may consider it composed of a large number of luminous 
points; each point will appear to the eye at its proper 
place, which will be at the place where the rays from that 
point meet; and an image of the complete object will 
result. 

Necessarily in this, and in all cases where the rays of 
light are not changed in direction in passing from the 
object to the eye, the image of the object and the object 
itself will coincide, and the object will appear to be where 
it actually is. 

531. Images with Plane Mirrors. — If, however, the direc- 
tions of the rays are changed in their passage to the eye, 
the result is very different. Referring to Fig. 197, let L 



§531] 



REFLECTION OF LIGHT 



321 




be a luminous point, and mm' a mirror. Just as in Fig. 
196, the rays /and ^ enter the eye in a certain direction. 
The brain knows nothing about the point L or the 
waves before they reach the eye ; 
the ray / indicates that the wave is 
coming from the direction fL\ and 
g indicates it comes from gL' ; hence, 
necessarily, the luminous point ap- 
pears to be at L' where the two rays 
meet. 

It may be shown by experiment 
and also by geometry that L' is as far behind the mirror 
as L is in front of it, and that a line LL' would be 
perpendicular to the mirror mm' . Hence the position of 
the image does not change as the eye changes. 

Finally, just as before, if L were a luminous body, the 
eye would see an image of each point at its proper place 
behind the mirror so as to form there a complete image of 
the object. Thus, let AL (Fig. 198) 
represent an arrow, and assume it 
to be luminous ; according to the 
discussion above, A would appear 
to the eye placed at E to be at A' 
and L at L' ^ and every other point 
on AL would appear at its corre- 
sponding place on A' L' ^ and a com- 
plete image would be seen at A'L' . 
Having located the two ends of the image, as the arrow is 
straight, in order to complete the image we have only to 
connect the two ends with a straight line. 

The simplest way to locate the image produced by a 
plane mirror is to draw from desirable points of the object 
perpendiculars to the mirror and as far beyond as the 
respective points are in front of the mirror. The ends of 





322 LIGHT , [§§531-535 

these perpendiculars will be the location of the images of 
the points ; and if these images are connected by proper 
lines, the completed image will result. 

532. Diffusion of Light. — If the light falls upon a sur- 
face such as a piece of paper it will be irregularly reflected, 
because the reflecting surface will be comparatively rough. 

Thus, in Fig. 199, L represents the 
luminous point and ss' the surface 
greatly magnified. The rays after re- 
,5 flection are entirel}^ unsymmetrical, and 
Fig. 199. hQ'diV 110 such relation to each otliet* as 

before the reflection ; hence no image can be formed. 
The light, however, is reflected, but is scattered through- 
out surrounding space illuminating neighboring objects. 
This process of irregular reflection is called diffusion of 
light. It is the way in which the interiors of houses are 
usually lighted up by the sunlight. 

533. Reflection from Curved Surfaces. — Any rough sur- 
face, whether plane or curved, will of course diffuse the 
light ; but a curved surface, if smooth, will reflect more 
or less regularly and form images. The only curved sur- 
face we need discuss, however, is the spherical surface 
forming a concave or a convex mirror. 

534. Concave and Convex Surfaces. — If the surface in- 
volved curves inwardly — caves in — it is a concave 
surface ; if it curves outwardly, it is convex. This applies 
to all surfaces, whether smooth or rough, symmetrical or 
unsymmetrical. 

535. Spherical Mirrors. — If a concave surface is smooth, 
and forms a segment of a spherical surface, it is a concave 
spherical mirror. And similarly a smooth convex surface, 
forming a segment of a spherical surface, is a convex 
spherical mirror. 

Whenever we look into a spherical mirror we see 



535] 



BEFLECTION OF LIGHT 



323 



images of surrounding objects, just as we do with plane 
mirrors. But with spherical mirrors the images are always 
more or less distorted, and are us-j^ally larger or smaller 
than the object. And another striking difference between 
concave mirrors and plane mirrors is that when, in a dark- 
ened room, we reflect the light from a bright object with 
a concave mirror and hold a screen in the path of the 
reflected rays at a proper distance from the mirror, an 
image of the object Avill appear on the screen (Fig. 200). 




Fig. 200. 



This is because the rays from any point of the object, 
although diverging when striking the mirror, are caused by 
the curvature of the mirror to converge; and if the screen 
is held at the place where the rays meet, an image of the 
point will be formed on the screen. All of the light 
which strikes the mirror from the point is concentrated 
at the one point on the screen ; and this illuminates the 
point so much more than the other portions of the screen 
are illuminated that it appears decidedly brighter. And 




324 LIGHT [§§ 535-536 

as every point of the object thus forms its corresponding 
image, the result is a complete image of the object. 

536. Images of Points by Concave Mirrors. — In forming 
diagrammatically images of points with any proper appa- 
ratus, let it be borne in mind that it is necessary only to 
find where two rays from the point meet each other ; that 
place will be where the image of the point is located. The 
reason for this we can see better after constructing an 
image. Let us consider the case 
with a concave mirror. 

In Fig. 201, let X be a luminous 
point, mm' a concave mirror, and 
the center of curvature of the 
^^' " ■ *^ spherical surface of which mm' is 
a segment. If a ray passes from L through it will 
strike the mirror perpendicularly, as Oe is a radius of the 
sphere ; and, according to the law of reflection, the reflected 
ray wall coincide with the incident ray and will pass back 
through 0. The image of the point then will lie some- 
w^here on this line. 

Now the line Pg drawn through the center of curvature 
0, and the center of the mirror g^ is called the principal 
axis of the mirror ; and all rays, such as Xf, parallel to 
the principal axis are called parallel rays. Also, it 
happens that all such parallel rays after reflection cross 
each other at nearly the same point. This point is at p 
in the figure ; it is called the principal focus^ and it 
always lies midway between the centers of curvature and 
of the mirror. 

Hence, in order to follow the course of a second ray, 
we have only to draw the parallel ray Lf to the mirror, 
and when reflected it will pass through the principal focus 
and cross the other ray at L' . Then the image of L will 
be at L' . 



§§ 537-538] 



REFLECTION OF LIGBT 



325 




Fig. 202 



537. Cause of Images. — Not only may the image be 
thrown on a screen in the manner suggested, but, if the 
eye is properly placed, the image will be seen at the same 
place if the screen is removed. Or, wherever the eye may 
be placed, as already suggested, images will be seen of 
surrounding bodies. Let us now consider these images. 
And first why may we say that this 
point L' is the location of the image 
of L when the screen is removed? 
It may be shown geometrically that 
any ray from L striking the mirror ^' 
will be so reflected as to pass through 
L' or very near that point. So we may say the light 
which strikes the mirror from L is all concentrated at L'. 
If this is true, these same rays must pass on through 
X^ as shown in Fig. 202, and an eye placed in a position 
to receive the rays, as at U^ would be acted on exactly 
as though L' were the original source of the rays or the 
luminous point itself ; and, for the reasons given in 
detail in Art. 530, L' will be the location 
of the image. 

538. Complete Images by Concave 
Mirrors. — As suggested in Art. 531 in 
order to form a complete image of an 
object we have only to locate certain 
points and then connect them by suitable lines. And with 
a concave mirror we may do this as shown in Fig. 203. 
The three important facts to bear in mind are : 
The image of any point will he where any two rays from 
that point meet. 

The incident ray through the center of curvature coincides 
with the reflected ray. 

The parallel ray is reflected through the principal 
focus. 




Fig. 203. 



326 LIGHT [§§ 538-530 

These facts form the general foundation for the for- 
mation of images with concave and convex mirrors and 
with lenses. 

The student should not be disturbed because rays cross 
and even return over the same path. We have seen 
already how sound-waves in case of echoes return over the 
same path without interference ; and it is the same with 
light. After the interfering waves have passed each 
other they continue exactly as if there had been no inter- 
ference. The only way in which the interference is effec- 
tive is when two waves oppose each other just as they strike 
the retina of the eye. But with the enormous number 
affecting the eye the few that neutralize each other are 
unimportant. A little thought will convince one tliat 
in a city the air must be incessantly disturbed with sound- 
waves continually crossing and coinciding ; yet there is 
no trouble ordinarily in distinguishing the various sounds. 
With light-waves and heat-waves in the ether the com- 
plications must be far greater, as practically all bodies 
are sending these out at all times ; yet this causes no 
object to appear at all indistinct. In order to clearly 
realize why this can be so we have only to rise to a full 
appreciation of the second law of motion. This law states 
that each force acting on any object has its full effect 
entirely independent of the effect of any other forces. 
Every influence which is capable of affecting the ether 
in any way has its full effect without reference to the 
effect of any other influence. 

539. Conjugate Foci. — As we have seen, the principal 
focus is the point where the parallel, or principal, rays 
meet, and any focus is a point where rays coming from the 
same point of light meet. Thus, in Fig. 202, L' is the 
focus of the rays from L. Now, if we consider L' as 
the luminous point, it is evident the rays e and / will be 



§§ 539-542] REFLECTION OF LIGHT 327 

reflected from the mirror to i, and L will be the focus of 
L', In such a case, then, the object and the image are 
interchangeable. If L is the object, the image will be at 
L' ; if L' is the object, the image will be at L. These two 
points then are joined, or conjugated, by this relation, and 
they are called conjugate foci. Hence any two points are 
conjugate foci when rays of light from either will be 
focussed at the other. And this holds for all mirrors and 
lenses. 

540. Real Images. — Images are divided into two 
classes, real and virtual. A real image is one where the 
rays actually meet. Thus, in Fig. 203, A' L' is a real image 
of AL because the rays from any point of AL actually 
meet at its corresponding point or conjugate focus at A'L' . 

Evidently a real image may be thrown on a screen, 
because, if the rays actually meet at the place where the 
image is formed, a screen, if properly placed, will be 
illuminated by the rays. 

541. Virtual Images. — If the image is formed by pro- 
longing backward the rays until they meet it is a virtual 
image. Thus, in Fig. 198, the rays themselves do not meet 
at L^ and A'., and no actual or real image is formed ; but 
the action of the rays on the eye is such as to cause an 
image to appear at L'A'., which is virtually the same as a 
real image ; hence it is called a virtual image. Evidently 
such an image cannot be thrown on a screen, as there are 
no rays where the image appears to be to illuminate 
the screen. But it may be thrown v ,* 
on the retina, as the lens of the eye ^^_^>^ JL^-''""^' ; 
changes the diverging rays to con- ^-^^^^^^^^^^^^^ j 
verging rays. / "^ 

542. Virtual Images with Concave ^'''- ^^*- 
Mirrors. — If the object is placed between the principal 
focus and the mirror, as in Fig. 204, the ray from a 




328 LIGHT [§§ 542-544 

striking at/ will pass back through the center of curvature 
0, while the parallel ray at g will pass back through the 
principal focus p ; so that the two rays will not meet at all. 
But, as in Fig. 198, the image will be at L' where the 
rays prolonged backward will meet, and the image will 
be virtual. 

543. Images with Convex Mirrors. — We have now only 
to apply the foregoing suggestions in order to form images 
with convex mirrors. Referring to Fig. 205, let be the 

center of curvature of the mirror. A 
ray from L travelling toward will 
be reflected back on itself by the 
convex surface, because, as it is the 
prolongation of a radius, it must be 
-^ noK perpendicular to the surface. The 

parallel ray from Z is a prolongation 
of a parallel line striking the concave side, and hence 
must have for its reflected ray the prolongation of what 
would be the reflected parallel ray on the concave side, 
or g. The image of L then will be L\ as this is where 
the two reflected rays / and g meet when prolonged. 

Similarly A' is the image of A^ and A' L' will be the 
complete image ; which is virtual, upright, and diminished 
in size. A comparison of this with Fig. 204 will show 
that, if both sides of the mirror were reflectors, L and V 
would be conjugate foci. 

544. General Discussion of Images with Concave Mirrors. 
— We are now in a position to tell what kind of image 
will be formed when the object is placed in any position. 
Let us take first the concave mirror : 

If the object is placed so far away that all the rays will 
be practically parallel, evidently the image will be at the 
principal focus. If the object is 200 feet or more away, for 
all ordinary purposes the rays may be considered parallel. 



§§ 544-545] REFLECTION OF LIGHT 329 

As the object is brought nearer the mirror, the image 
will recede from the mirror ; it will be real, inverted, and 
diminished, but will increase in size until the center of 
curvature is reached, when it will coincide in position and 
size with the object, but will still be inverted. 

As the object is brought still nearer, the image will still 
recede, being real, inverted, and magnified ; and when the 
object reaches the principal focus, the image will be located 
an infinite distance away. 

As the object is brought still nearer, the image will also 
move nearer, being virtual, erect, and magnified ; but it 
will gradually diminish until, when the object is against 
the mirror, the image and object coincide throughout. 

Some of these effects can be very satisfactorily shown 
with an ordinary concave mirror ; but the image will be, 
in many cases, distorted and indistinct owing to imperfec- 
tions in the mirror, or to the fact that the object is not a 
mere point, or to what is called spherical aberration. 

545. Spherical Aberration. — If we draw a semi-spheri- 
cal mirror, as shown in Fig. 206, and let fall upon it 
parallel rays, it is at once 
evident, from the law of 
reflection, that the reflected 
rays near the outer edge of 
the mirror will not pass to 
the principal focus. And it 
will be the same if the rays, 
instead of being parallel, 
diverge from any point in front of the mirror, — the outer 
rays will focus nearer the mirror. This failure of the 
outer rays to focus coincidently with the inner ones is 
called spherical aberration^ and is the cause of more or 
less indistinctness of the images. 

Aberration of this nature does not occur if the mirror is 




Fig. 206. 



330 ' LIGHT [§§545-546 

parabolic instead of spherical, and the better class of 
mirrors are so made. As the surface of a comparatively 
small section of a sphere is nearly parabolic in form, the 
aberration is greatly reduced by using spherical mirrors of 
slight curvature. 

546. Discussion of Images with Convex Mirrors. — All 
images with convex mirrors will be virtual, not inverted, 
and diminished. When the object is removed so far as to 
cause only parallel rays to fall upon the mirror, the image 
will be at the principal focus and extremely small. 

As the object approaches the mirror, the image will also 
approach and will increase in size until the object reaches 
the mirror, when the object and the image will practically 
coincide in position and form. 

Spherical aberration is effective with convex mirrors 
just as with concave mirrors, and is reduced or removed 
in the same manner. 

EXERCISES 

1. If the angle of incidence of a ray of light is 28°, what 
angle will the ray form with the reflecting surface ? 

2. If the angle formed by the incident ray and the reflected 
ray is 64°, what angle does the reflected ray form with the 
reflecting surface ? 

3. If two rays from the same point of light form an angle of 
2°, and strike upon a plane mirror, what angle will the back- 
ward prolongations of the reflected rays form ? 

4. Draw the necessary lines and form an image of an arrow 
23roduced by a plane mirror. 

5. Similarly, draw the image of an arrow produced by a con- 
cave mirror. 

6. Make a diagram showing a real image formed by a con- 
cave mirror. 

7. Make a diagram showing a virtual image with a convex 
mirror. 



§§ 547-548] REFRACTION OF LIGHT 331 

8. A ray parallel to the principal axis forms an angle of 65° 
with the tangent to a concave mirror where the ray strikes the 
mirror. What angle does it form with a line from that point 
through the center of curvature ? 

SECTION 4. REFRACTION OF LIGHT 

547. Speed of Light in Transparent Bodies. — When light 
falls upon a transparent body like a piece of glass, although 
a portion of the light is reflected, the greater portion passes 
on through the body apparently undisturbed. Careful in- 
vestigation, however, shows that in such a case the light 
is interfered with ; it is retarded somewhat. Its speed in 
glass, for instance, is considerably less than in air. 

This is so with all transparent bodies, they retard the 
motion of the light ; even air itself is no exception. And 
the amount of retardation is somewhat proportional to 
the density of the body, though this is true only in a 
general way. 

548. Refraction of Light. — As a 
result of this retardation when a beam 
of light strikes obliquely a transparent 
body, as indicated in Fig. 207, its 
direction is changed. The portion at 
a is held back, so that when h reaches 
the body the wave-front has taken the 

position a'¥, and the direction of the beam is changed as 

shown in the figure. This 
changing of the direction 
of light upon entering a 
transparent body is called 

L«- Fxn, 9n« ^•/!?% refraction of light. 

This effect may be seen 

by looking at any object through a three-sided prism ; the 

object will appear displaced, as indicated in Fig. 208, 





332 LIGHT [§§548-552 

because the ray of light coming from the object has its 
direction changed, and the eye sees the object as if it were 
located on the backward prolongation of the ray which 
enters the eye. 

549. Optical Density. — The amount of refraction differs 
with the nature and condition of the substance. It de- 
pends very much on the density of the substance, but not 
altogether. For convenience the term optical density is 
used to indicate the refractive power of substances ; the 
better refracting substances are said to be optically denser. 

550. Direction of Refraction. — As shown in Fig. 207, the 
beam on striking the refracting surface is pulled around 
deeper into the substance which refracts it. If, as shown 

in Fig. 209, we draw a line perpendicular 
to the surface which refracts, we may say 
the ray is refracted toward the perpen- 
dicular. That is, when a ray passes 
obliquely from any substance, — say air, 
— into one which retards the light more^ it 
is refracted toward the perpendicular. 
Conversely, it is evident that if a beam 
passes into a substance which retards it less^ the side first 
emerging will travel faster, and the beam will turn away 
from the perpendicular. 

551. Angle of Refraction. — Just as the angle formed by 
the normal and the reflected ray is the angle of reflection, 
so the angle formed by the normal and the refracted ray is 
the angle of refraction. Thus COB, Fig. 209, is the angle 
of refraction. And, just as with the angle of reflection, 
the angle of refraction lies in the same plane as the angle 
of incidence. 

552. Index of Refraction. — Obviously, the angle of 
refraction is not equal to the angle of incidence ; however, 
it happens that there is a certain relation between the two 




§§ 552-553] REFRACTION OF LIGHT 333 

angles which always exists, no matter what the angle of 
incidence may be, provided the density of the substance 
remains the same. This relation is called the , 

B 1 A 

index of refraction for the particular substance \ j 
involved, and may be described as follows : \o 

If on the ray BOO, Fig. 210, at points B T 

and 0, equal distances from 0, perpendiculars j \ 

BA and OB be drawn to the surface normal, ^• 

the ratios between such perpendiculars will ^^^' ^^^' 
always be the same, no matter what the angles may be, 

AB 

so long as the substance is unchanged. Thus -t^— 1-52 

for ordinary crown-glass, no matter whether the angle of 
incidence is 2° or ten or twenty times that amount. And 
this ratio is called the index of refraction. We may say, 
then, when equal hypothenuses are laid off on the rays, the 
ratio between the legs opposite the angles of incidence and of 
refraction is the index of refraction. 

As the refraction is caused by the change in speed of the 
light when passing into the new medium, it is not strange 
that there is a direct relation between the index of refrac- 
tion and the respective speeds in the two media. The 
relation is that the ratio between the two speeds is equal 
to the ratio between the two legs referred to above, and 
hence is equal to the index of refraction. 

If the index of refraction is known for any substance, we 
can determine how much will be the deviation of any ray 
striking its surface ; and we know whether it is a poorer 
or a better refractor than some other substance of which 
the index is known. 

553. Laws of Refraction. — From the foregoing we may 
derive the following laws of refraction : 

Radiant energy passing obliquely into an optically denser 
substance is bent toward the normal to its surface, and when 



334 LIGHT [§§ 553-555 

passing into a rarer substance it is bent away from the 
normal. 

Tlie angles of incidence and of refraction always lie in the 
same plane. 

When the rays form equal hypothenuses^ the ratios between 
the legs opposite the angles of incidence and of refraction 
luill be constant for any given substance. 

From these laws of refraction flow certain consequences, 
which have important bearings on scientific investigations, 
and which continually affect, directly or indirectly, our daily 
lives. Some of these consequences we will now consider. 

554. Media with Parallel Surfaces. — Let us first con- 
sider the passage of a ray of light entirel}^ through a 
medium the surfaces of which are parallel, — for instance, 

a piece of ordinary plate-glass. Refer- 
ring to Fig. 211, suppose the light to 
be travelling from ^ to ^ ; then angles 
/ and g will be equal, as they are alter- 
nate interior angles. Hence e and h 
must be equal, as the light would take 
the same path travelling from B to A 
Fig. 211. ^g from A to B^ and the same relation 

must exist between h and / as between e and g. But if 
this is true, A produced must be parallel to B^ and the 
ray, although shifted sideways somewhat, is not changed 
in direction. 

This shifting may be readily shown, experimentally, by 
looking obliquely through a piece of plate-glass at a 
straight line drawn on a piece of paper so that part of 
the line projects beyond the glass. The portion seen 
through the glass will be shifted away from the remainder. 

555. Media with Non-parallel Surfaces. — If, however, 
the bounding surfaces of the medium are not parallel, as 
in the case of a three-sided prism, the rays are changed 




§§ 555-557] EEFBACTION OF LIGHT 335 

in direction on passing through the medium. Thus, in 
Fig. 208, the ray, in passing into the prism, will be re- 
fracted downward toward the normal 7^, and on passing 
out, — as it goes then into the air, which is a poorer re-- 
f ractor, — it will be refracted downward again, away from 
the normal n' ^ so the direction of the entering ray will be 
very different from that of the emerging ray. 

This fact, that light may be changed in direction by 
passing it through a transparent substance, is the basis of 
many valuable optical instruments, such as microscopes, 
telescopes, cameras, and so on. For all these instruments, 
however, lenses are used instead of prisms, and these we 
shall now consider, carrying with us constantly the effect 
of parallel and non-parallel bounding surfaces on the rays 
of light. 

556. Lenses. — So far we have considered only plane 
bounding surfaces. With lenses at least one of the sur- 
faces is curved ; and, just as 
with curved mirrors, the curved 
surface is usually a segment of 
the surface of a large sphere; 
while the edges are always circu- 
lar. The forms of lenses which we will consider are 
shown in Fig. 212, and are named as follows : 

1. Double-convex. 4. Double-concave. 

2. Plano-convex. 5. Plano-concave. 

3. Concavo-convex. 6. Convexo-concave. 

557. Center of Curvature of Lenses. — As the phrase in- 
dicates, the center of curvature of any lens is that point 
which is at the center of the sphere of which the side of 
the lens being considered forms a segment. Necessarily 
a lens with two curved surfaces has two centers of curva- 
ture. 






336 LIGHT [§§558-561 

558. Focus of Lens. — Suppose a ray of light passes from 
the point i, Fig. 213, to the double-convex lens at B\ 

just as with a prism, it will 
be bent downward at each 
surface of the lens, and will 
pass onward in the direction 
L' , Another ray striking at 
D will be bent upward at each surface, and will cross 
the other ray at L' . Now if the lens is properly con- 
structed, all other rays passing from L through the lens 
will pass through this same point L' ; and hence such point 
is called the focus of the point X, and 
the image of L will be located at this 
point, or focus. 

If, however, the lens is doxihlQ-concave^ 
the rays will be bent away from each 
other, and will not cross, as shown in 
Fig. 214. In such case, just as with convex mirrors, the 
light will focus at L' where the rays produced backward 
would cross, and all images will be virtual. 

559. Conjugate Foci. — Evidently if L\ Fig. 213, were 
a luminous point, rays from it passing through the lens 
would meet at L. Hence, as with mirrors, the two points 
are interchangeable ; the object may be at either point and 
the image will be at the other. They are, therefore, con- 
jugate foci. 

560. Principal Focus. — When the rays striking the lens 
are parallel, as is the case with the sun's rays, the point 
where they meet, as with mirrors, is called the principal 
focus. For most purposes the rays from any object two 
hundred feet or more away may be considered as parallel. 

561. Converging and Diverging Lenses. — A little thought 
will show that all lenses which are thicker in the middle 
than at the edges, such as the plano-convex, will cause 



§§ 561-562] REFRACTION OF LIGHT 337 

rays passing through to converge more than they did 
before; for this reason such lenses are called converging 
lenses. On the contrary, those which are thinner in the 
middle will cause the rays to diverge more, and hence are 
called diverging lenses. With converging lenses the 
principal focus is on the side opposite the source of light ; 
with diverging lenses it is on the same side as the light. 
In fact, diverging lenses must always focus on the side of 
the lens from which the rays come. 

562. Optical Center. —The ray AB, Fig. 215, will 
necessarily pass through the lens without refraction, as 
the portions of bounding surfaces through which it passes 
are parallel. For the same reason the ray CD will pass 
through without change of 
direction. And the point 
where these rays cross is called 
the optical center. It is the 

• At, 1. 1 • 1 Fig. 215. 

point through which any rays 

passing will not be changed in direction because the 

bounding surfaces through which the rays pass will be 

parallel. It is true that most rays passing through this 

point will be refracted; but, as explained in Art. 554, 

this will not permanently change the direction of the 

rays. 

The optical center is at the center of the lens only when 
the two surfaces are curved equally. For other lenses it 
may be found by drawing two radii from 
one center of curvature, and then two 
radii respectively parallel to the first two 
from the other center. The place O 
where the lines which connect the ends 

Fig. 216. 

of these radii cross, as shown in Fig. 216, 
will be the optical center, because the tangents at the ends 
of either pair of parallel radii will be parallel. 





338 LIGHT [§§ 563-564 

563. Principal and Secondary Axes. — The straight line 
AB^ Fig. 215, passing through the center of curvature 
and the optical center of the lens is the principal axis ; 
and all straight lines such as CD passing through the optical 
center, except the principal axis, are called secondary axes. 

Evidently rays along the secondary axes are never 
changed in direction while passing through the lens, 
though they may be shifted slightly sidewise. 

564. Formation of Images. — Just as with mirrors, the 
place where the rays from a luminous point meet, after 
passing through a lens, will be the location of the image of 
the point. In the formation of images, then, it is neces- 
sary only to follow the course of two rays, and find where 
they meet. We can easily follow the ray which passes 
along the secondary axis, as it goes through the lens with- 
out any refraction. We can also follow the ray parallel 
with the principal axis, as it goes, after refraction, through 
the principal focus, provided we know where the principal 
focus is. 

In case of ordinary lens glass the principal focus of a 
double-convex lens is practically at the center of curvature ; 
and as the center of curvature is easily found when a 
drawing is made of a lens, we shall have no trouble in 
forming, by diagrams, images with such lenses. With 
other lenses, however, the determination of the principal 
focus is beyond the scope of this work, so we will not at- 
tempt the formation of images with 
other than double-convex lenses of 
ordinary glass. 

In Fig. 217 let C be the center of 
curvature and the optical center. 
AA^ and LL^ are rays from the ends of the arrow along 
secondary axes, and ABA\ LBL' show the course of the 
parallel rays before and after passing through the lens. 




§ 665] BEFRACTION OF LIGHT 339 

565. Discussion of Images with Double-convex Lenses. — 

When the object is so far away as to cause the rays to be prac- 
tically parallel, the image formed by a double-convex lens 
will be at the principal focus, and will be extremely small. . 

As the object approaches the lens, the image will recede 
from the lens, will increase in size, and will be inverted 
and real. 

When the object is at the center of curvature, the image 
will be infinitely distant. 

As the object approaches the lens from the center of 
curvature, the image will pass to the same side of the lens 
as the object, and hence will be virtual; it will also be 
upright and enlarged. 

As it approaches the lens it will decrease in size, until 
on reaching the lens the image and object will, practically, 
coincide throughout. 

EXERCISES 

1. When light passes from a vacuum into air, why is it re- 
fracted towards the normal, if it is refracted away from the 
normal in passing from water into air ? 

2. If the principal focus of a lens is at its center of curva- 
ture, where would it be and why, if the lens and focus were in 



a vacuum 



3. If two right-angled triangles have always equal hypothe- 
nuses, how will the ratio between the two vertical legs change 
as the hypothenuses increase ? 

4. Article 552 says to lay off equal distances on the lines 
representing the rays. If an inch were taken as the unit 
instead of a centimeter, how would it affect the index of 
refraction ? Why ? 

5. Considering the sun's rays falling on a water surface, 
how do the rates of change of the angles of incidence and of 
refraction compare when the sun is rising ? when it is setting ? 

6. Are the two angles in such a case ever equal in Boston'^ 
are they ever equal anywhere ? 



3-10 LIGHT [§ 566 

7. If the index of refraction of crown glass is 1.52, what is 
the speed of light in the glass ? 

8. What is the speed of light in water ? (See table, page 375.) 

9. Show by diagram the location of the optical center of a 
convexo-concave lens. A double-convex lens. 

10. What determines the ratio between the lengths of the 
image and object with a double-convex lens ? Show this by a 
diagram. 

11. If an object is 12 inches from its image on a screen, and 
the lens is 8 inches from the screen, where may the lens be 
placed to produce another image ? 

12. What would be the relative areas of the two images ? 

13. Draw a diagram of a double-convex lens, a point of light, 
and its image, with the necessary rays. On the same diagram 
indicate another point of light near the first, and draw rays and 
form its image. Connect the two points with a straight line. 

14. Draw a diagram of a double-convex lens, an arrow, and 
its image. 

15. As a point of light approaches a converging lens, do the 
refracted rays converge more, or less ? Does this cause the 
image to recede, or to approach ? to increase, or to diminish ? 

16. If the sun's rays fall on a convex lens when it is under 
water, why will they focus farther away from the lens than 
usual ? 

17. When a piece of glass is placed in water of equal optical 
density it becomes invisible. Why so ? 

18. If two plano-convex lenses are placed with their flat 
faces together, will a ray passing through these faces be 
changed in direction ? Why ? 

19. Where, then, is the principal focus of an ordinary crown- 
glass plano-convex lens ? 

SECTION 5. APPLICATIONS OF REFRACTION 

566. Sight. — The most important, and perhaps the 
most interesting, application of the laws of refraction is 
to the eye. The sense of sight depends upon the refrac- 



§§ 566-567] APPLICATIONS OF BEFRACTION 341 

tion of light by the lens of the eye. The rays of light, 
diverging from the object which is seen, pass through the 
lens of the eye, which acts as a double-convex lens, con- 
verging the rays and forming a real image of the object 
upon the retina. The effect upon the retina is then trans- 
ferred by the optic nerve to the brain, where it is inter- 
preted by the mind as a vision of the object. 

567. The Eye. — As indicated in Fig. 218, the eye is 
nearly spherical in form. This allows it to be turned 
freely in its socket, so that it may be faced toward the 
object to be seen. The principal 
parts, so far as optics are concerned, 
are the sclerotic coat, the iris, the 
crystalline lens, and the retina. 

The sclerotic coat S is an opaque 
coat which forms the outer surface of 
the eye, preventing light from entering 
except through a circular opening in 
front which forms a window for the passage of light from 
the object to the interior of the eye. 

The iris / is a film forming a circular curtain around 
the opening in the sclerotic coat, which so regulates the 
size of the opening that the proper amount of light may 
enter. 

The crystalline lens C is located immediately behind the 
iris, in the center of the opening. It is double-convex in 
form, and serves the purpose of converging the rays of 
light and forming upon the retina an image of the object 
viewed. 

The retina i2 is a screen at the back of the eye, of proper 
nature to receive the image and allow the effect to be 
transmitted by the optic nerve to the brain. 

The optic nerve transfers the effect of the image from 
the retina to the brain. 




342 LIGHT [§§ 568-571 

568. The Crystalline Lens. — This lens is not only 
double-convex, but it is so constructed that the amount 
of convexity may be changed at will, to a limited extent ; 
that is, it may be flattened or thickened. This decreases 
or increases the convergence caused by the lens, so that 
distant objects, as well as near objects, may be made to 
focus clearly upon the retina, without changing the dis- 
tance from the retina to the lens. Every person is thus 
able to " accommodate " his eyes to different distances. 

569. Near-sightedness. — Frequently, however, the dis- 
tance from the lens to the retina is so great that the person 
is unable to flatten the crystalline lens sufficiently to cause 

the image to reach the retina, even 
when the object is near, the image 
being formed in front of the retina, 
as shown in Fig. 219. Such persons 
are called near-sighted, because they 
must bring the object abnormally 
close to the eye in order to see it. The remedy in such 
case is a pair of glasses that will cause the rays of light 
to diverge more before they strike the lens ; that is, glasses 
that are diverging lenses. 

570. Far-sightedness. — On the other hand many per- 
sons are unable to thicken or increase the convexity of 
the lens, sufficiently to bring 
the image as far forward as the 
retina, especially with near ob- 
jects, the image being formed 
behind the retina, as shown in ^^' 

Fig. 220. Such persons are called far-sighted. In such 
case the remedy is a pair of converging glasses. 

571. Old-sightedness. — A third case of inability to focus 
near objects occurs frequently in old age or low nervous 
condition, when the power of accommodation is so weak- 





§§ 571-573] APPLICATIONS OF REFRACTION 343 

ened that the lens cannot be properly adjusted by the 
controlling muscles. The remedy in such a case is usually 
a pair of convex, or converging, lenses, which reduces the 
effort required to accommodate. 

572. The Camera. — There is much similarity between 
the eye and the ordinary photographing apparatus, or 
camera. Each has the converging lens upon which light 
from the object strikes and is refracted; also the dark 
chamber through which the rays pass; and the screen at the 
back upon which the image is formed. The only general 
difference is the effect upon the screen at the back. With 
the eye the screen, which is the retina, is only temporarily 
affected by the image ; with the camera the screen, which 
is a film of some chemicals sensitive to light upon a plate 
of glass or other material, is permanently affected. The 
screen is called the plate. 

Figure 221 gives an idea of the apparatus. The camera 
is so placed that an image of the object L will be formed 
by the lens I on the plate P. The lens being uncovered for 
an instant, each part of the substance forming the film on 
the plate is affected in proportion to the intensity of light 
falling upon it. The plate, be- 
fore the light falls upon it, is 
opaque ; after the exposure to 
the lis^ht, and after it has been 

11 1 1 „ 1 1 Fig. 221. 

properly "developed, the plate 

forms what is called a negative ; and the different parts 
of the negative are more or less transparent, depending on 
the intensity of the light which has fallen on each particu- 
lar part. By means of the negative, pictures of the origi- 
nal object are printed by allowing light to pass through 
it and affect paper which is made sensitive to light. 

573.' Simple Microscope. — The purpose of the micro- 
scope is to throw upon the eye enlarged images of objects 




344 



LIGHT 



573-574 




Fig. 222. 



An ordinary 



which are too small to be seen otherwise, or images of 
portions of larger objects, so that the details may be more 
clearly seen. 

If a double-convex lens is placed between 
the eye and an object L (Fig. 222) so that the 
object is between the lens and the principal 
focus, the object will appear to the eye to be 
located at L' and to be enlarged. Such a 
lens, placed in a frame suitable for holding it, 
is called a simple microscope. Such micro- 
scopes are frequently used by watchmakers 
and repairers, and by others engaged at work 
requiring the fine details to be clearly seen, 
reading-glass is also a simple microscope. 

574. The Compound Microscope. — A compound micro- 
scope is, practically, a combination of two simple micro- 
scopes, each of which assists in magnifying the object 
which it is desired to see. 

To understand the arrangement, it should 
be borne in mind that we may have an 
image of another image^ just as we may have 
an image of an object. In Fig. 223 the 
lens I forms an image L' of the object iy, 
and then the lens V forms of the image L' 
an image L'\ which is seen by the eye 
placed at E. The dotted lines passing 
from the ends of L' indicate the course 
rays would take if L' were a luminous 
body. The effect on the eye in such case 
is the same as if L' were an object with L" 
its image ; but, as each lens magnifies, the effect is much 
better than with the single lens. 

The lens I is much the smaller, and is called the objective ; 
the other lens is called the eyepiece. 




Fig. 223. 



575-576] APPLICATIONS OF BEFEACTION 



345 



575. The Telescope. — The purpose of a telescope is to 
cause distant objects to appear brighter and enlarged, so 
that details may become visible. Increased brightness is 
secured by using a large objective lens; more rays of 
light will strike this lens than would strike the eye, and 
the brightness is proportional to the amount of light 
striking the lens, as, practically, all the rays striking the 
objective strike the eye. Hence the ratio between the area 
of the objective and the opening of the eye gives the ratio 
between the brightness with and without the telescope, 
provided there is no difference in the size of the image 
produced on the retina. 

In Fig. 224, I represents the objective and V the eye- 
piece. The eyepiece is used, as with the microscope, to 
magnify the image L' formed by the objective. As 
the telescope is used 
to view distant 
objects, frequently 
many thousand 
miles away, the 
rays striking the objective are so nearly parallel that the 
image is located at the principal focus, and is necessarily 
extremely small. Hence a diagram such as Fig. 225 is 
not a correct representation ; it shows the conditions when 
the object is but a few feet from the objective. A correct 
diagram would be impracticable. 

576. The Opera-glass. — If, instead of the converging 

eyepiece, a diverging lens 
is used, an erect image of 
the object will be produced, 
as indicated in Fig. 225. 
Here, too, the arrangement 
is distorted, the object being 

much closer than usual to the objective. This was the 




Fig. 224. 




Fig. 225. 



346 



LIGHT 



[§§ 576-577 



earliest form of the telescope, being first used by Galileo. 
If two such telescopes are joined together with their axes 
parallel, an enlarged image of distant objects will be 
produced in each eye. Such an apparatus is the ordinary 
opera-glass of to-day. 

577. The Optical Lantern. — The projection or optical 
lantern is an apparatus for projecting on a screen an en- 
larged image of an object without decreasing its bright- 
ness ; in fact it frequently greatly increases the brightness 
of the object. When the object is partly transparent, such 
as a drawing or photograph on glass, called a lantern slide, 




Fig. 226. 



the increase in brightness is produced by placing the object 
in front of a powerful light, such as the ordinary arc light, 
and allowing the transmitted light to fall upon the screen ; 
while the enlargement is produced by placing the screen 
upon which the image falls a considerable distance from 
the object, interposing between the object and the screen 
suitable lenses. Figure 226 shows the relative positions of 
the light, the object, and the lenses. The lenses CC are 
called condensing lenses, and are used to collect as much 
light as possible to be thrown upon the screen, and to 
properly direct the rays through the object. S is the object, 
usually a lantern slide. L is an arc light with the carbons 



§§ 577-578] APPLICATIONS OF BEFBACTION 347 

tipped so as to face the brightest light toward the lenses. 
D is the dynamo which generates the current for the light. 
is the objective which focusses the rays on the screen S' , 

When the object is opaque, like an ordinary painting on 
oil-cloth or paper, the light is thrown upon the object, the 
image of which is to be projected, so that it is reflected 
from the object through the lens and on to the screen. 
With this arrangement a greatly enlarged image of any 
opaque body may be projected upon the screen. 

578. Total Reflection. — When a tumbler full of water 
is held overhead, the upper surface of the water, if viewed 
through the water in the right direction, acts as a perfect 
reflector. This is called total reflection. It is, however, a 
special case of refraction. 

Consider la^ Fig. 227, an object moving from L through 

a dense medium into a rarer medium. When the end a 

enters the rarer medium it will travel so much faster than 

the other end that the object will 

turn and be in the position a'V 

before the portion at I reaches the 

rarer surface. As I will still be 

retarded more than a the object will 

, T . Fig. 227. 

turn still farther and plunge again 

into the denser medium as indicated. If this is so for a 

moving object, we may assume that a ray of light would, 

for the same reasons, on striking the rare surface, be 

turned back again into the denser medium. In such 

a case the surface would act as an ordinary reflector. 

Evidently total reflection occurs whenever the angle of 

refraction is more than 90°, because the surface forms an 

angle of 90° with its normal, and the refracted (in this 

case reflected) ray must be in the same medium as the 

incident ray. So when light strikes the rarer surface 

from a neighboring point the effect must be as shown 




348 



LIGHT 



[§§ 678-579 





Fig. 228. 



Fig. 229. 



in Fig. 228, some of the rays being reflected, the rest 

being merely 
refracted. 

In case of 
total reflec- 
tion the light 
scarcely dimin- 
ishes in inten- 
sity ; and it is, 

therefore, common to use prisms so arranged as thus to 
reflect light for various purposes. The general method 
is shown in Fig. 229. 

579. Natural Applications of Refraction. — Many curious 
atmospheric phenomena are due in part, at least, to refrac- 
tion. Mirages are caused sometimes when the light from 
distant objects is totally reflected on passing through the 
dense lower air to a rarer surface above. The refractive 
effect of the air causes the sun to be seen earlier in the 
gH^ morning and later in the evening 

than it otherwise would, as shown, 
greatly exaggerated, in Fig. 230, in 
which S represents a ray of sun- 
light, and E the earth, surrounded 
by its atmosphere which is denser 
nearer the surface. Rainbows are 
caused by refraction and reflection, 
as will be explained in the following 
section. The wavy appearance of 
hot air arising from a stove or other heated object is 
caused by the rays of light being refracted while passing 
through layers of air of different densities. Bodies of 
water appear shallower than they are, when viewed side- 
wise, because light coming to the eye from beneath the 
water is refracted as it passes into the air» 




Fig. 230. 



§580] CHROMATICS 349 

EXERCISES 

1. What effect does flattening a double-convex lens have on 
the location of the image ? Why ? 

2. If the upper side of a vertical converging lens is flattened 
more than the lower side, what effect will it have on the 
appearance of the image? 

3. If the upper side of the crystalline lens of a near-sighted 
person were thinner than the lower, how should his glasses be 
ground ? 

4. What is the magnifying power of a simple microscope 
when the object is 2 centimeters from the lens and the image 
is 8 centimeters from the object ? 

5. With a telescope is the image actually larger than the 
object ? How do the images on the retina with and without 
a telescope compare in size ? 

6. If the image on the retina is 30 times as large with the 
telescope as without, and the objective is 20 times as large as 
the opening of the iris, does the object appear brighter with or 
without the telescope ? 

7. While under the water, which could see with the naked 
eye objects under the water better, a near-sighted or a far- 
sighted person, and why ? 

8. Would a person under water looking upward be able to 
see objects near the horizon ? Why ? 

9. What would be the shape of the opening through which 
he could see ? 

10. Why is it that the rays of sunlight do not ordinarily 
travel to the earth in straight lines ? 

11. Why do round fish-globes sometimes set fire to neigh- 
boring objects ? 

SECTION 6. CHROMATICS 

580. Chromatics. — So far we have considered light 
without reference to colors. We will now consider the 
various Qolors, — how they are produced naturally and arti- 



350 LIGHT [§§580-583 

ficially, what is their cause, and their relations to each 
other. All such considerations fall properly under the 
heading Chromatics. 

581. Composition of White Light. — We have seen under 
Sound how extremely complicated are, what appear to be, 
very simple sounds. A chord played on a musical instru- 
ment usually consists of several fundamental notes and 
innumerable harmonics or overtones. In fact it is seldom 
indeed that simple sounds are heard. It is the same with 
light ; the apparently simple white light of the sun may 
be readily decomposed into a large number of colored 
lights. The rainbow, with which every one is familiar, is 

caused by light from the sun being 
so decomposed. Let us consider 
in detail the decomposition of 
white light. 

582. Dispersion. — If a beam of 
sunlight L is allowed to fall upon 
a glass prism, as shown in Fig. 231, 
the beam will not only be refracted 
but will also be spread out., or dispersed ; and on falling 
upon the screen S^ a long band of light will be seen in- 
stead of a small spot such as is seen on the prism. This 
spreading out of the light is called dispersion. 

583. Spectrum. — In such a case the band of light, instead 
of being white like sunlight, will have all the colors of the 
rainbow, and in the same order as they appear in the rain- 
bow. Such a band of colored light is called a spectrum of 
the sunlight, or a solar spectrum. A spectrum of any light 
may be formed in a similar manner. If the original light is 
white, such as the incandescent electric light, the spectrum 
will be colored similar to the solar spectrum. If, however, 
the original light is colored, the spectrum will be mucli 
shorter than with the white light, usually only hands of 




Fig. 231. 




§§ 683-585] CHROMATICS 351 

color; and there will be but two or three colors at the 
most, frequently only one. 

584. Analysis of Light. — Sir Isaac Newton, in 1666, 
was the first person to intelligently analyze light by means- 
of a prism. He allowed sunlight to pass into a darkened 
room through a hole in the shutter, and formed a spectrum 
on a screen by means of a prism. To determine the cause 
of the peculiar effect, 
he allowed the blue 
light of the spectrum 
to pass through a 
hole in the screen, 
and again refracted 
it with a prism, as 
indicated in Fig. 
232. He refracted 
successively, in a similar manner, each of the other colors, 
and found that the colors that were refracted most in the 
original spectrum were refracted most the second time; 
and from this he concluded that the spectrum was formed 
because each color was refracted more or less than the 
others, and thus its own position in the spectrum was 
determined by the amount it was refracted, or, as it is 
called, its ref Tangibility. 

585. Synthesis of Light. — If, instead of allowing the 
dispersed light to fall upon a screen to form a spectrum, 
it is caused to fall upon another prism properly placed 

and of suitable form, as indicated in Fig. 233, 
the various colors will again be refracted, but 
so as to continue in the same direction as 

Fir 233 

_J_ that of the original beam, and the result will 
be a white image similar to the image thrown on the first 
prism. The various colors may thus be recomposed into the 
original light. This may be called the synthesis of light 




352 LIGHT [§§ 585-588 

When white light is thus formed by synthesis, Newton's 
conclusions are fully verified. That white light is com- 
posed of numerous colored lights is shown by actually so 
composing the white light ; and that each color has its own 
refrangibility is shown by the fact that in passing, as it 
were, back through the prism, each is refracted differ- 
ently from every other and the same as it was originally 
refracted. 

586. Cause of Dispersion. — A century and a half passed, 
however, after Newton's investigations before an entirely 
satisfactory theory of the dispersion of light was offered. 
It will be sufficient here to state that the cause of disper- 
sion lies in the fact that the waves which give the different 
colors of which white light is composed, are retarded 
differently when passing through any substance, and as 
refraction depends on this retardation, evidently the wave 
which is retarded most will be refracted most. 

587. Order of Dispersion. — Whenever a spectrum is 
formed by any means, the colors arrange themselves in a 
definite order. Taking the seven colors which are usually 
seen, the order in which they occur is as follows : 

Red, orange, yellow, green, blue, indigo, violet. 

And invariably the red is refracted least, and the violet 
most. So we conclude that red is retarded least, or travels 
most rapidly through the refracting substance, and violet 
travels most slowly. 

588. Cause of Colors. — The question arises in such a 
discussion as this. What is there about the light-wave 
which .causes the different colors ? This we are now in a 
position to answer. The complexity of the sounds which 
we hear is due to the fact that they are composed of a 
large number of simple sounds, variously combined ; and 
differences in the simple sounds are due to differences in 
the length of the sound-waves^ which in their turn are due 



§§588-589] CHROMATICS 353 

to differences in the frequencies of vibrations of the sono- 
rous bodies. It is very similar with light. The complexity 
of the lights which we see is due to a number of simple 
lights, or colors, variously combined ; and it is no doubt- 
true that differences in these simple lights are due to 
differences in their light-waves, and these in their turn 
are due to differences in the frequencies of vibrations of 
the molecules or atoms producing the waves. 

As the frequency with which the sound-waves strike 
upon the ear determines the pitch of the sound, so the 
frequency with which the light- waves strike upon the eye 
determines the color of the light. 

It must not be supposed, however, that there are only 
seven different colors, and thus only seven different light- 
wave lengths. On the contrary, there is almost an infinite 
number of colors, or at least shades of colors, and a wave- 
length for each shade. The large number of shades is 
easily noticed in an ordinary rainbow, and is very striking 
in a good spectrum. In neither case, however, are the 
shades distinct, but the colors gradually merge, by means 
of their shades, into each other. 

589. Length of Light-waves. — As it is impossible to 
measure directly the frequency of a vibrating molecule, 
the frequency is usually found by measuring the length 
of the light-wave, and dividing the speed of light by 
this length. So it is usual to speak of the wave-length 
causing any particular color rather than of the fre- 
quency. 

A simple color, or a monochromatic light, strictly speak- 
ing, would be one caused by a single wave-length. But 
there are probably few, if any, such cases; all ordinary 
colors, at least, are easily shown to be composed of more 
than one wave-length, and hence of more than one shade or 
tint. But the wave-lengths usually given for the various 
2a 



354 



LIGHT 



[§§ 589-591 



colors are the lengths producing the central tints of the 
general color. 

The methods of measuring wave-lengths depend upon 
the interference of light-waves. 

590. Interference of Light- waves. — When two light- 
waves coincide, we may have a reinforcement or a weak- 

^-. -^ ening of the effect, exactly as with 

\^ V-/ \J sound-waves. If the equal waves w 
wf\ j\ r\ and«^' (Fig. 234) coincide, the result- 

ant effect will be the wave W. If, 




:oooooo 



Fig. 234. 



Fig. 235. 



however, one of them drops back one-half a wave-length, 
so the two take the positions w and w^ (Fig. 235), the 
resultant effect will be practically W, or no wave at 
all. This latter case is ordinarily spoken of as interfer- 
ence of light-waves. 

591. Measurement of Light-waves. — There are several 
methods for measuring wave-lengths of light, most of 
them, however, beyond this work. One simple method, 
and perhaps the most accurate, is by the use of Michelson's 

interferometer. 

Referring to Fig. 236, a ray 
of light Z, as nearly monochro- 
matic as possible, is allowed 
to fall upon a semi-transparent 
mirror iw, one-half the light 
passes through, strikes the 
mirror m', and is reflected by 
m' and m to the eye at E. The 
other half of the light is reflected by m to the mirror m" 
and by m'^ back to ??^, and a portion goes through m to 



E 
Fig. 236. 



§§ 591-594] CHROMATICS 355 

the eye. So the two waves coincide between m and U, and 
will reinforce or interfere according to whether or not the 
crests fall together. Now by sliding m" backward, the 
wave between m" and the eye may be shifted backward, 
and as it is slowly shifted there will be alternately inter- 
ference and reinforcement of light, producing dark and 
bright effects visible at U. By counting the number of 
dark effects appearing, the number of half-wave lengths 
that m" is moved, is determined, because the light goes to 
m'' and back ; and by measuring with a micrometer disk 
and screw the distance 7n" is moved, the wave-length may 
be readily determined. 

Light-waves are extremely short, the longest, those of 
red light, being about .0007 mm., and the shortest, violet, 
about .0004 mm. (See table, page 375.) 

592. Range of Vision. — Between the red and the violet 
light, which form the extremes of the spectrum, there are, 
as already suggested, innumerable tints or shades, any one 
of which, if sufficiently intense, may be seen by the normal 
eye. But any ether- wave the length of which is greater 
than those of red or less than those of violet light, does 
not affect the eye. In other words, there is a range of 
vision as well as of hearing, any waves falling outside the 
range having no effect on the eye. 

593. Heat-waves. — Nevertheless, there are innumerable 
ether-waves longer than those producing red light. These 
are the heat-waves already described. Instead of affecting 
the eye they affect the skin. It is a matter of everyday 
experience that the same object may give out both heat- 
waves and light-waves. In fact most objects emitting light- 
waves emit also heat-waves; but many objects give out 
one without the other. 

594. Actinic Waves. — There are also innumerable waves 
shorter than those producing violet light. These are 



356 LIGHT [§§ 594-596 

called actinic waves. They are the waves which produce 
chemical effects on various substances, such as the sensi- 
tive plates and paper of the photographer. They are 
also effective in producing growth of vegetation. Most 
luminous bodies emit actinic waves; but such waves are 
frequently produced without light-waves. In case of 
incandescent solids, we have produced heat-waves, light- 
waves, and actinic waves. 

595. Continuous Spectrum. — When a spectrum, pro- 
duced with a prism or otherwise, has no colors or shades 
missing, it is called a continuous spectrum. In such a case 
all the wave-lengths from those of red light to those of 
violet light are produced by the luminous body. 

596. Rainbow. — The rainbow is a striking illustration 
of a continuous spectrum. It results whenever the sun 
i?s shining near the horizon and the rain is falling near the 
opposite horizon. As illustrated in Fig. 237, a ray of 
light S^ passing from the sun to a drop of water o, is 

refracted and dispersed on entering 
^ "* Z^^^P\ ^^® drop, is reflected by the back 

side of the drop, and is further 

refracted and dispersed on leaving 
'^ ^^"^ ^^^^ drop ; so a spectrum of the 

sun is produced; and if the drop 
is in just the right position, one of the colored rays will 
strike the eye at E^ the other colors passing above or 
below the eye. If a green ray strikes the eye, various 
higher drops will cause the orange, yellow, or red to 
strike the eye, and various lower drops the blue, indigo, 
and violet. So the entire spectrum is thrown upon the 
retina of the eye. As the drops fall, others take their 
places ; and drops either side cause a prolongation of the 
spectrum in a circular form, frequently to the horizon. 
A secondary bow is often formed. This is produced 





§§ 596-598] CHROMATICS 357 

in about the same way, the passage of the rays being as 
indicated in Fig. 238. This second bow is in no way 
related to the primary how. 

As a necessary condition for a 
rainbow, the sun, the eye, and the 
center of the bow must lie in the 
same straight line. For this rea- 
son rainbows are never produced 
when the sun is high. 

597. Bright-line Spectrum. — 
The spectra of many luminous bodies have some colors 
missing, and consist of narrow bands of colored light, with 
dark unlighted spaces between, as indicated in Fig. 239 ; 
or there may be but a single band or colored line. This 

kind of spectrum is called the hrigJit- 
■^H|H^n^|^H line spectrum. It is usually pro- 
duced when any colored light is used 
as the luminous source. When 
Newton, as suggested in Art. 584, allowed the single 
colors of the first spectrum to pass through the second 
prism, he produced a bright-line spectrum consisting of 
a band or line of the particular color involved. 

All incandescent gases under ordinary pressure give 
bright-line spectra. All like gases under similar con- 
ditions of pressure and temperature give like spectra ; 
but the spectra of no two unlike gases are alike. By in- 
creasing the pressure on the gas the lines are broadened 
into bands, indicating an increased variety of wave-lengths, 
but all about the same length. If, however, the gas is 
compressed sufficiently, the spectrum becomes continuous 
as if the gas were a solid or a liquid. 

598. Dark-line Spectrum. — A third form of spectrum 
is the dark-line spectrum. It resembles the bright-line 
spectrum in so far as it consists of mere lines, but the 



358 LIGHT [§§ 598-600 

lines are dark instead of bright, and between the lines 

there are colored instead of dark spaces. It resembles the 

continuous spectrum in so far as it consists, usually, of 

all the ordinary colors. The dark 

spaces are narrow lines crossing 

Fig 240 ^^^^ colored bands, as indicated in 

Fig. 240. 

This is frequently spoken of as the absorption spectrum, 

as it is a phenomenon of absorption; hence in order to 

understand its cause we shall need to understand this 

subject. 

599. Absorption of Light. — When light-waves fall upon 
an opaque body, some of them are reflected and the rest 
absorbed, none being transmitted through the substance. 
When the body is transparent, some of the waves are 
reflected and practically all the rest are transmitted, few 
or none being absorbed. So, ignoring for convenience the 
reflected light, we may have either all or practically none 
of the light absorbed. Again, if the light falls upon a 
piece of blue glass, the blue light alone is transmitted, 
the rest being absorbed. If it falls upon the yellow flame 
produced by burning sodium, the yellow light alone is 
absorbed by the flame, the rest being transmitted. So we 
have in the one case all the colors but one absorbed, the 
rest being transmitted, and in the other case all the 
colors transmitted but one, that being absorbed. And we 
may have innumerable other cases, involving various kinds 
or degrees of absorption. 

600. Cause of Absorption. — If the light can pass througii 
some substances with scarcely any hindrance, and is en- 
tirely destroyed by others no thicker or denser, it must be 
that the molecules of the opaque substance in some way 
use up the energy contained in the light-waves, while tlie 
molecules of the transparent body do not. Careful inves- 



§§ 600-601] CRBOMATICS 359 

tigation has shown, as we shall see in the next article, that 
a light wave is absorbed if it attempts to pass through a 
substance whose molecules vibrate in unison with the wave; 
that is, if the frequency of the wave and of the normal 
vibration of the molecules is the same, the energy of the 
wave will be absorbed by the molecule, and the vibra- 
tions of the molecules will increase accordingly. And 
that this must be true follows from the discussion in 
Art. 293. When light is absorbed the absorbing sub- 
stance is warmed ; the motion of its molecules is 
increased; and if a light- wave imparts to a molecule 
increased motion, it performs work, and its energy is used 
accordingly. 

That sound-waves are so absorbed may be shown by 
attempting to pass a sound-wave through a number of 
wires tuned in unison with the wave ; the original sound- 
wave will be destroyed, as its energy will be used in setting 
up sympathetic vibrations in the wires. Or any sonorous 
body, causing sympathetic vibrations in any other body, 
will lose its energy faster than if no such vibrations were 
caused. 

601. Emission and Absorption. — The sodium flame which, 
as suggested, absorbs the yellow light, is itself intensely 
yellow ; in fact it is exactly the same color as that which 
it absorbs ; and hence it absorbs waves of the same fre- 
quency as that which it emits^ and thus supports the above 
theory of absorption. This is true of all gases under 
ordinary pressure, they all emit the same wave-length as 
they absorb. And it is immaterial what the temperature 
of the gas may be, — when cold it absorbs the same wave- 
lengths as it emits when incandescent. In fact the wave- 
lengths which it emits when cold, are, undoubtedly, the 
same as when hot; as, like sound-waves, differences in 
intensity of light or heat are due to differences in amplitude 



360 LIGHT [§§601-603 

of vibration, and not at all to differences in frequency or 
wave-length. 

It should be constantly borne in mind, however, that 
little or nothing is known about the vibrations of mole- 
cules, or whether heat and light are caused by their vibra- 
tions. But as the effect produced upon our senses is 
similar to the effect which such vibrations might produce, 
we are warranted in assuming the vibrations to exist, 
especially as no facts of consequence are inconsistent with 
such assumption. And as such assumption assists greatly 
in understanding and investigating the principles of heat 
and light, this is a sufficient warrant, even though there 
be no truth in the assumption. 

The fact that gases absorb certain wave-lengths forms 
the basis of the dark-line or absorption spectrum ; and the 
fact that they absorb when cooler the same wave-lengths that 
they emit when incandescent^ forms the basis of an ex- 
tremely important application of this spectrum, as we shall 
now see. 

602. Absorption Spectrum. — Evidently if we form on a 
screen a continuous spectrum, and then place between the 
screen and the source of light an object which absorbs any 
of the colors of light, the colors absorbed will disappear 
from the spectrum, leaving in their places dark lines, pro- 
vided the object itself does not emit as much light as it 
absorbs. This is the principle of the absorption spec- 
trum. It may be more fully understood by considering 
some practical applications. 

603. Spectrum Analysis. — If the spectrum results from 
the fact that each color and shade has a different wave- 
length from every other, and that the refrangibility of 
the wave is in the order of its length, each shade must 
have its own place on the spectrum. For instance, the 
peculiar shade of yellow similar to that of the sodium 



§§603-605] CHROMATICS 361 

flame must always occupy its own special place in the 
yellow portion of the spectrum. And it must also be 
true that each gas, under similar conditions of pressure, 
emits its own particular wave-length and shade. Hence 
if the peculiar shade emitted by any gas, and its position 
in the spectrum, are known, it may also be known whether 
such gas is producing in whole or in part the light which 
causes the spectrum. For instance, if it is desired to test 
a substance to see whether it contains sodium, we have 
only to burn the substance so as to turn it into an incan- 
descent gas, and then notice whether the yellow peculiar 
to sodium is present in the spectrum. This is what is 
called spectrum analysis — analyzing substances by means 
of the spectrum in order to determine the elements of 
which the substance is composed. 

604. Analysis by Absorption Spectrum. — In order to 
analyze substances it is frequently convenient to use the 
absorption spectrum, and often no other method can be 
used. In this case if it is desired to know whether 
sodium, for instance, is in a substance, we may place it, 
in the state of a gas, between an incandescent solid and 
its spectrum. It will then absorb from the waves emitted 
by the solid those waves which are in unison with its own 
molecules and produce dark lines in the spectrum; from 
the position of these dark lines in the spectrum it may be 
determined whether or not the substance contains sodium. 

605. Spectroscope. — Spectrum analysis, however, is not 
so simple as is implied by the above general statements. 
Delicate apparatus and much experience are necessary. The 
apparatus ordinarily used is called the spectroscope^ and is 
shown in Fig. 241. It consists of three parts : the appa- 
ratus for controlling the light before refraction^ the apparatus 
for refracting the lights and the apparatus for controlling the 
light after refraction. 



362 



LIGHT 



[§§ 605-606 



The light is controlled before refraction by the colli- 
mator C. This consists of a brass tube, at the outer end 
of which is a narrow slit through which the light passes, 
while at its inner end is a converging lens with its prin- 
cipal focus at the slit so that it will transmit the light as a 
beam of parallel rays. 




Passing from the collimator the beam strikes the refract- 
ing apparatus, which consists ordinarily of a glass prism P, 
or, if much dispersion is desired, several prisms properly 
arranged. 

From the prism the light passes into a telescope T which 
magnifies the spectrum to be viewed by the eye, the screen 
on which the spectrum is formed being ordinarily the 
retina of the eye. 

606. Fraunhofer Lines. — The spectrum of sunlight is a 
remarkable case of absorption spectrum. If it is strongly 



A «B c 



Eb 













] 


















ill ill iH 





RED ORANGE YELLOW GREEN 



Fig. 242. 



dispersed, the spectrum will show innumerable dark lines 
scattered throughout its entire length, as shown in Fig. 242. 



§§ 606-607] CHEOMATICS 363 

These lines are named after Joseph Fraunhofer, of Bava- 
ria, who early in the nineteenth century made the first 
thorough investigation of them. Fraunhofer, however, 
was unable to explain the cause of the lines, and nearly, 
half a century passed before they were satisfactorily ex- 
plained. 

After our previous discussion the cause is easily under- 
stood. The sun and earth are surrounded by atmospheres 
of various gases ; these act as absorbers of certain portions 
of the sun's light ; and whenever any particular wave- 
length is absorbed, necessarily at its proper place in the 
spectrum, as no light falls there, a dark line appears. 

A strongly magnified solar spectrum shows thousands 
of these lines ; and they are no doubt due mainly to 
absorption by the sun^s atmosphere. As the gases absorb 
those waves which they emit, and as the exact position in 
the spectrum of the waves they emit may be experimen- 
tally determined, evidently a dark line appearing in the 
solar spectrum will indicate by its position what gas in the 
sun's atmosphere has caused the line. Thus the composi- 
tion of the atmosphere of the sun and many of the stars 
has been determined. The fact that in such cases a dark- 
line spectrum is produced indicates also that the atmosphere 
is cooler than the body of the sun or star, as otherwise the 
atmosphere would emit as much light as it absorbs. 

Many other important astronomical facts are determined 
by means of the absorption spectrum. For instance, the 
lines in the solar spectrum produced by sunlight reflected 
from the moon are just the same as those produced by 
direct sunlight, indicating that the moon has little if any 
atmosphere. 

607. Motion of the Stars. — An extremely important 
application of the spectrum to the stars is the determina- 
tion of the direction and speed of their motions. If the 



364 LIGHT [§§ 607-608 

position of the dark lines, or of any shade, is due to the 
wave-lengths, evidently if the wave-length causing any 
particular line could be changed^ increased or decreased, 
the dark line would be shifted along one way or the other 
in the spectrum. Now, while the actual wave-length of 
any light-wave cannot be changed, still, if the luminous 
body is moving toward the screen upon, which the light 
is striking, each succeeding wave has a shorter distance 
to travel before striking the screen, and hence, in effect, 
the waves are shortened, because the frequency of impact 
on the screen is increased ; and, necessarily, in such a case, 
if a spectrum of the light is formed, any dark or bright 
line will occupy a position different from what it would 
if the luminous source were at rest or were moving away 
from the spectrum. 

By this principle, which is called the Doppler principle, 
much valuable astronomical information has been gained 
in recent years. The details of the applications, however, 
are beyond this work. 

608. Fundamental Colors. — We have seen that when 
the spectrum of white light is passed through a second 
prism, the various colors may be combined so as to form 
white light. If the same colors in similar proportions are 
thrown together on the same surface in any way, white 
light will result. Because of this, the spectrum, or rain- 
bow, colors have been called the fundamental colors. But 
numerous other color combinations will produce white 
light, and there is no particular reason for calling any 
one set more than any other the fundamental colors. 
Red, green, and violet will produce white light, and 
these are often called the fundamental colors, as they 
are the basis of a prominent color theory. There is no 
good scientific reason, however, for calling any colors 
fundamental. 



§§ 609-612] CHROMATICS 365 

609. Complementary Colors. — White light may be pro- 
duced by only two colors, and by many combinations of 
only two colors. In such cases the two colors are called 
complementary/ colors. Thus orange and blue are comple- 
mentary ; also yellow and indigo, green and purple ; 
purple, by the way, being a color that is entirely missing 
in the spectrum. 

610. Colors by Combinations. — The colors themselves 
may be formed by combining other colors, just as white 
light is so formed. Thus violet and red produce purple ; 
red and yellow produce orange; green and violet, light 
blue ; yellow and blue, light green. And any color may 
be produced by properly combining red, green, and violet. 

611. Colors by Reflection. — Most of the colors which 
are to be seen on all sides are produced, partly at least, by 
reflection. If white light falls on certain surfaces, some 
of the colors may be absorbed and the rest reflected ; and 
the reflected light will give the object its color. Those 
objects which appear red, for instance, reflect only the red 
light, or such colors as will give to the eye the appearance 
of red. If the light falling on a surface is itself colored, 
the reflected light will be affected accordingly. If all the 
light is reflected, it will be the same as the incident light ; 
if some colors are absorbed, that reflected will be, of course, 
not that which would produce white light when combined 
with the absorbed light, but that which would produce, 
when so combined, the same color as the incident light. 
Because of this, many objects appear differently by gas- 
light than by sunlight or electric light, gas-light being 
decidedly reddish. 

612. Colors by Transmission. — The beautiful colors of 
transparencies and stained glasses are due to the fact that 
some of the colors are absorbed by the glass and the 
others are transmitted to the eye. Blue glass transmits 



366 LIGHT [§§ 612-614 

the blue light and absorbs or reflects the others ; it looks 
blue by reflected light because it reflects mainly blue 
light. The orange-yellow of the atmosphere late in the 
afternoon is due to the absorption or reflection of all the 
other colors by the greater thickness of the atmosphere 
which the sun's rays are then passing through. The blue 
of the sky is due to the blue light being reflected by the 
particles floating in the air. 

613. Colors by Absorption and Reflection. — In most cases 
of reflection the light penetrates into the object somewhat 
and is there reflected, and in thus passing into and out of 
the substance much of the light is absorbed that would 
otherwise be reflected. In fact the surface-reflected 
light is mainly white light; so the color of the body is 
largely, if not altogether, due to the internally reflected 
light. And the smaller the amount of surface reflection 
the purer the colors, as they are not then dimmed so much 
by the white reflected light. This is shown by velvets, as 
the peculiar surface allows almost no surface reflection. 

614. Colors by Interference. — The colors of soap-bubbles 
when about to break, the colors of certain oils spread on 
water, of many birds' feathers, of many beetles and flies, 
and many other beautiful colors, are due to interference. 
In all such cases the light which is reflected from within 
the substance, usually from the surface farthest from the 
light, interferes with the light reflected from the first 
surface ; so some of the colors of the white light are de- 
stroyed, leaving the remainder to pass to the eye. Thus 
with the oil on water, some light is reflected from the 
upper surface and some from the lower ; on leaving the oil 
the two waves coincide and those waves with crests that 
coincide with troughs of other waves are destroyed, and 
their corresponding colors are missing. To produce this 
result, very thin films of the substance are required, — not 



§§6U-615] CHEOMATICS 367 

thicker than one or two wave-lengths. The beautiful 
colors of polarization, which are too abstruse to discuss 
here, are the result of interference ; and this is probably 
the cause of opalescence. 

615. Colors by Photography. ^ Many efforts have been 
made to photograph the colors of objects, but no one has 
succeeded in making such colors permanent. Some photo- 
graphs of colors have been made, but they were only 
temporary, disappearing in a few days at most. All color 
effects in case of photography are produced by mechanical 
contrivances; and it is not likely to be otherwise, as 
there seems to be no scientific basis for the assumption 
that a color can be made to reproduce itself by the light 
which it casts upon any chemical. 



EXERCISES 

1. Are the rays of the sun after passing through a prism 
parallel, couverging, or diverging? How are the rays of the 
same color from the sun ? 

2. If the spectrum of the sun were thrown on a lens and the 
rays thus all brought to the same focus, what would be the 
color of the image ? 

3. What kind of a lens would be required in such a case ? 

4. If the shorter wave-lengths were refracted least, what 
would be the order of the colors of the spectrum ? 

5. How many " octaves " of light are there in the range of 
vision ? 

6. What is the length of a middle C sound-wave at 0° in 
terms of the yellow light-wave ? 

7. How many sodium light-waves strike the eye per second? 

8. A sodium light is placed in front of an incandescent 
solid. What kind of a spectrum will be formed if the sodium 
light illuminates the screen more than the solid ? if it illumi- 
nates it less ? if the same ? 



368 LIGHT 

9. Are any wave-lengths of the continuous spectrum missing 
from the rainbow ? 

10. Why can we not tell by spectrum analysis of v/hat sub- 
stance the body of the sun is composed ? 

11. If the spectrum of a star gave a sodium dark-line, what 
would be the effect on the position of the line if the star were 
moving toward the earth ? 

12. What would be the color of a pure red object viewed 
through a blue glass ? Why ? 

13. Why do blue objects look less green by electric light 
than by ordinary gas-light ? 



APPENDIX 



Metric Units of Length 

Millimeter (mm.) = .1 cm. 
Centimeter (cm.) = 1 cm. 
Decimeter (dm.) = '1^0^^cm\ 
Meter (m.) = 100 cm. 

Kilometer (km.) = 1000 m. 

Metric Unit of Capacity 
Liter (1.) = 1000 cm.^ 

Metric Units of Weight 

Milligram (mg.) = .001 g. 
Centigram (eg.) = .01 g. 
Decigram (dg.) — ".Tg. 
Gram (g.) =1 g. 

KilogTam (kg.) = 1000 g. 

Relations between English and Metric Units 

Inch (in.) = 2.54 cm. 

Pound (lb.) = 453.6 g. 

Gallon (gal.) = 3.79 1. 

Meter (m.) = 1553163.5 red (cadmium) light-waves 

Formulas 

(tt = 3.1416. r = radius.) 

Circumference of a circle = 2 7rr 
Area of a circle = irr'^ 

Surface of a sphere = 4 Trr^ 

Volume of a sphere = ^ irr^ 

2 b 369 



370 



APPENDIX 



Weights of Various Substances 



1 ft.^ of water at 4° weighs 
1 ft.8 of air at 0° and 76 cm. weighs 
1 cm. 3 of air at 0° and 76 cm. weighs 
I 1. of hydrogen at 0° and 76 cm. weighs 



62.425 lb. 
.08073 lb. 
.001293 g. 
.0897 g. 



Densities or Specific Gravities 

The following tables give the weight in grams per cm.^ The 
numbers should be considered only as approximations, as the density 
varies with the temperature and with the specimen. 



solids 



Agate 2.615 

Alum 1.724 

Aluminum 2.670 

Amber 1.078 

Antimony, cast .... 6.720 

Arsenic 5.700 

Asphalt 2.500 

Beeswax 0.964 

Bismuth 9.800 

Bone 1.900 

Brass, cast 8.3 + 

Brass, sheet 8.440 

Brick 1.6 to 2.000 

Bronze 8.700 

Butter 0.942 

Canada balsam .... 1.070 

Camphor 0.988 

Carbon, gas 1.800 

Cedar, American .... 0.554 

Chalk 1.8 to 2.800 

Cherry ....... 0.710 

Chestnut 0.606 

Coal, anthracite . 1.26 to 1.800 

Coal, bituminous . 1.27 to 1.423 

Cobalt 8.800 

Cork 0.240 



Copper, cast 8.830 

Copper, sheet 8.900 

Diamond 3.530 

Ebony 1.187 

Elm 0.579 

Emery 3.900 

Feldspar 2.600 

Galena 7.580 

German silver 8.620 

Glass, green 2.640 

Glass, crown 2.520 

Glass, flint . . . . 3.0 to 3.600 

Gold, 18-carat 14.880 

Gold, pure 19.300 

Gypsum, crystal . . . . 2.310 

Granite 2.650 

Graphite 2.500 

Gunpowder 2.030 

Guttapercha 0.970 

Human body 1.070 

Ice 0.918 

Iceland spar 2.700 

Iron, cast . . . 7.100 to 7.600 

Iron, wrought 7.800 

Iron, steel 7.790 

Ivory 1.920 



APPENDIX 



371 



Lead 11.350 

Lignum vitae 1.333 

Limestone 3.180 

Magnesium 1.750 

Mahogany . . . 0.560 to 0.852 

Maple 0.755 

Marble 2.720 

Nickel 8.570 

Oak, red 0.850 

Oak, white 0.779 

Oak, live, dry 1.068 

Paraffine .... 0.824 to 0.940 

Phosphorus 1.830 

Pine, white, dry .... 0.554 

Pine, yellow, dry .... 0.461 

Platinum 21.500 

Poplar 0.389 

Porcelain, china .... 2.380 

Potassium 0.865 



Quartz 2.650 

Rock salt 2.257 

Sand, quartz 2.750 

Silver, 0.925 fine ... . 10.380- 

Silver, pure 10.570 

Slate 2.880 

Sodium 0.970 

Steel 7.790 

Sugar, cane 1.593 

Sulphur 2.033 

Tallow 0.940 

Tar 1.015 

Tin, cast 7.290 

Walnut 0.680 

White metal, Babbitt . . 7.310 

AVillow 0.585 

Zinc, cast 6.860 

Zinc, rolled 7.200 



LIQUIDS 



Acetic acid at 

Alcohol, absolute 

Alcohol, amyl 

Benzine 

Carbon bisulphide 

Chloroform 

Ether 

Glycerine 

Hydrochloric acid 

Kerosene . . . 

Mercury at 0° C 

Milk (cow's) '' 

Molasses . . 



15° C 



1.053 
0.7937 
0.809 
0.890 
1.270 
1.499 
0.720 
1.260 
1.220 
8-0.804 
13.596 
1.030 
1.426 



Naphtha 0.748 

Nitricacidat 15°C. . . . 1.520 

Oil, castor " "... 0.970 

Oil, linseed, boiled . . . 0.940 

Oil, olive, at 15° C. . 0.915 

Oil, turpentine " " . . 0.872 

Petroleum 0.836 

Sulphuric acid .... 1.840 

Vinegar 1.026 

Water, sea, at 0° C. . . . 1.026 

Water " " ... 0.999 

Water at 4° C 1.000 

Water at 100° C 0.958 



The above densities and the following specific heats are from 
Nichols, Smith, and Tui'ton's Manual of Experimental Physics. 



372 



APPENDIX 



Coefficients of Linear Expansion 

(Brass, German silver, glass, and steel vary somewhat.) 

Aluminum .... 0.000023 

Brass 0.000019 

Copper 0.000017 

German silver . . . 0.000018 

Glass 0.000085 

Gold 0.000015 



Iron .... 


. . . 0.000012 


Lead .... 


. . . 0.000009 


Silver . . . 


. . . 0.000019 


Steel. . . . 


. . . 0.000013 


Tin .... 


. . . 0.000023 


Zinc .... 


. . . 0.000029 



Specific Heats referred to Water 



solids 



Aluminum 0.2185 

Antimony 0.0507 

Bismuth 0.0305 

Brass 0.0940 

Copper 0.0933 

German silver .... 0.0946 

Glass 0.1900 

Gold ....... 0.0320 

Zinc . . . 



Ice 0.5040 

Iron 0.1125 

Lead 0.0317 

Nickel 0.1100 

Platinum 0.0320 

Quartz 0.1910 

Silver 0.0559 

Tin 0.0559 

... 0.0935 



liquids 



Alcohol at 17° C. . . . 
Carbon disulphide at 15° C. 
Chloroform " " 

Ether " " 



0.580 
0.230 
0.233 
0.530 



Glycerine, 0°-100° C. . . 0.555 

Mercury at 15° C. . . . 0.033 

Turpentine at 17° C. . . 0.430 

Water 1.000 



gases at constant pressure 



Air 0.2375 

Hydrogen 3.4090 

Nitrogen 0.2438 



Oxygen 0.2175 

Steam 0.4805 



APPENDIX 



373 



Table of Natural Sines and Tangents 



Angle 


Sine 


Tangent 


Angle 


Sink 


Tangent 


Angle 


Sine 


Tangent 





0.000 


0.000 


31 


0.515 


0.601 


62 


0.883 


1.881 


1 


0.017 


0.017 


32 


0.530 


0.625 


63 


0.891 


1.963 


2 


0.035 


0.035 


33 


0.545 


0.649 


64 


0.899 


2.050 


3 


0.052 


0.052 


34 


0.559 


0.675 


65 


0.906 


2.145 


4 


0.070 


0.070 


35 


0.574 


0.700 


66 


0.914 


2.246 


5 


0.087 


0.087 


36 


0.588 


0.727 


67 


0.921 


2.3.56 


6 


0.105 


0.105 


37 


0.602 


0.754 


68 


0.927 


2.475 


7 


0.122 


0.123 


38 


0.616 


0.781 


69 


0.934 


2.605 


8 


0.139 


0.141 


39 


0.629 


0.810 


70 


0.940 


2.747 


9 


0.156 


0.158 


40 


0.643 


0.839 


71 


0.946 


2.904 


10 


0.174 


0.176 


41 


0.656 


0.869 


72 


0.951 


3.078 


11 


0.191 


0.194 


42 


0.669 


0.900 


73 


0.956 


3.271 


12 


0.208 


0.213 


43 


0.682 


0.933 


74 


0.961 


3.487 


13 


0.225 


0.231 


44 


0.695 


0.966 


75 


0.966 


3.732 


14 


0.242 


0.249 


45 


0.707 


1.000 


76 


0.970 


4.011 


15 


0.259 


0.268 


46 


0.719 


1.036 


77 


0.974 


4.331 


16 


0.276 


0.287 


47 


0.731 


1.072 


78 


0.978 


4.705 


17 


0.292 


0.306 


48 


0.743 


1.111 


79 


0.982 


5.145 


18 


0.309 


0.325 


49 


0.755 


1.150 


80 


0.985 


5.671 


19 


0.326 


0.344 


50 


0.766 


1.192 


81 


0.988 


6.314 


20 


0.342 


0.364 


51 


0.777 


1.235 


82 


0.990 


7.115 


21 


0.358 


0.384 


52 


0.788 


1.280 


83 


0.993 


8.144 


22 


0.375 


0.404 


53 


0.799 


1.327 


84 


0.995 


9.514 


23 


0.391 


0.424 


54 


0.809 


1.376 


85 


0.996 


11.43 


24 


0.407 


0.445 


55 


0.819 


1.428 


86 


0.998 


14.30 


25 


0.423 


0.466 


56 


0.829 


1.483 


87 


0.999 


19.08 


26 


0.438 


0.488 


57 


0.839 


1.540 


88 


0.999 


28.64 


27 


0.454 


0.510 


58 


0.848 


1.600 


89 


1.000 


57.29 


28 


0.469 


0.532 


59 


0.857 


1.664 


90 


1.000 


Infinity 


29 


0.485 


0.554 


60 


0.866 


1.732 








30 


0.500 


0.577 


61 


0.875 


1.804 









374 



APPENDIX 



Dimensions and Functions of Copper Wires 



„. 


Diameter 






Eesistance at 


24= C. 


z 


g i 




ClIiCULAR 

Mils 


Feet per 
- Lb. 








=: § 




Mils 


Milli- 
meters 


Ohms per 
1000 Ft. 


Feet per 
Ohm 


Ohms 
per Lb. 


< <* 


8 


128.490 


3.264 


16509.00 


20.05 


0.643 


1555.000 


0.01289 


46.1 


9 


114.430 


2.907 


13094.00 


25.28 


0.811 


1233.300 


0.02048 


38.7 


10 


101.890 


2.588 


10381.00 


31.38 


1.023 


977.800 


0.03259 


32.5 


11 


90.742 


2.305 


8234.00 


40.20 


1.289 


775.500 


0.05181 


27.3 


12 


80.808 


2.053 


6529.90 


50.69 


1.626 


615.020 


0.08237 


23.0 


13 


71.961 


1.828 


5178.40 


63.91 


2.048 


488.250 


0.13087 


19.3 


14 


64.084 


1.628 


4106.80 


80.59 


2.585 


386.800 


0.20830 


16.2 


15 


57.068 


1.450 


3256.70 


101.63 


3.177 


306.740 


0.33133 


13.6 


- 16 


50.820 


1.291 


2582.90 


128.14 


4.582 


243.250 


0.52638 


11.5 


17 


45.257 


1.150 


2048.20 


161.59 


5.183 


192.910 


0.83744 


9.6 


18 


40.303 


1.024 


1624.30 


203.76 


6.536 


152.990 


1.3312 


8.1 


19 


'35.390 


0.899 


1252.40 


264.26 


8.477 


117.960 


2.2392 


6.7 


20 


31.961 


0.812 


1021.50 


324.00 


10.394 


96.210 


3.3438 


5.7 


21 


28.462 


0.723 


810.10 


408.56 


13.106 


76.300 


5.3539 


4.8 


22 


25.347 


0.644 


642.70 


515.15 


16.525 


60.510 


8.5099 


4.0 


23 


22.571 


0.573 


509.45 


649.66 


20.842 


47.980 


13.334 


3.2 


24 


20.100 


0.511 


504.01 


819.21 


26.284 


38.050 


21.524 


2.8 


25 


17.900 


0.455 


320.40 


1032.96 


33.135 


30.180 


34.298 


2.4 


26 


15.940 


0.405 


254.01 


1302.61 


41.789 


23.930 


54.410 


2.0 


27 


14.195 


0.361 


201.50 


1642.55 


52.687 


18.980 


86.657 


1.7 


28 


12.641 


0.321 


159.79 


2071.22 


66.445 


15.050 


137.283 


1.4 


29 


11.257 


0.286 


126.72 


2611.82 


83.752 


11.940 


218.104 


1.2 


30 


10.025 


0.255 


100.50 


3293.97 


105.641 


9.466 


349.805 


1.0 


31 


8.928 


0.227 


79.71 


4152.22 


133.191 


7.508 


557.286 


0.84 


32 


7.950 


0.202 


63.20 


5236.66 


168.011 


5.952 


884.267 


0.70 


33 


7.080 


0.180 


50.13 


6602.71 


211.820 


4.721 


1402.78 


0.60 


34 


6.304 


0.160 


39.74 


8328.30 


267.165 


3.743 


2207.98 


0.50 


35 


5.614 


0.143 


31.57 


10501.35 


336.810 


2.969 


3583.12 


0.42 


36 


5.000 


0.127 


25.00 


13238.83 


424.650 


2.355 


5661.71 


0.35 



APPENDIX 



375 



Speed of Sound 



Media Temp. 

Air 0° 

Brass 17° 

Copper 17° 

Glass 17° 

Iron ,17° 

Lead 17° 

Maple 

Oak 

Pine 

Steel 17° 

AYater 8.1° 



Meters per sec. 



. . . 332 
3200 to 3500 

. . . 3555 

. . . 5000 

. . . 5125 

. . . 1300 

. . . 4110 

. . . 3850 

. . . 3320 

. . . 5100 

. . . 1435 



Mean Index of Refraction 





Index of 




Index of 




Eefractiox 




Eefraction 


Air 


1.000294 


Glass, crown . . . 


1.52 


Alcohol 


1.372 


Glass, flint .... 


1.60 


Canada balsam . . . 


1.54 


Ice 


1.31 


Carbon disulphide 


1.68 


Turpentine. . . . 


1.48 


Diamond 


2.47 


Water 


1.336 


Ether 


1.36 







Wave-length of Light 

Unless otherwise specified the central portion of the color is re- 
ferred to. 

Millimeters 

0.0005872 
0.0005972 
0.000643847 



Millimeters 

Violet 0.0004059 

Indigo ..... 0.0004383 

Blue 0.0004960 

Green 0.0005271 



Yellow (sodium) 

Orange .... 

Red (cadmium) 

Red 0.0007000 



INDEX 



[Numbers refer to Pages] 



Aberration, spherical, 329. 
Absolute amount of heat, 158. 

temperature, 157. 

units of force, 39. 

zero, 15 7. 
Absorption, of light, 358. 

spectrum, 358. 
Accelerated motion, 25. 
Acceleration, 25. 

due to gravity, 58. 

of falling bodies, 56. 

Unit of, 39. 
Acoustic telephone, 302. 
Actinic waves, 355. 
Adhesion, 16, 17. 
Air columns, length of, 292. 

Vibrating, 291. 
Air-pump, 119. 
Alternator, 255. 
Amalgamation of zinc, 201. 
Ammeter, 228. 
Ampere, 206. 
Amplitude, 66. 
Analysis, of light, 351. 

Spectrum, 360. 
Angles, of incidence, 318. 

of reflection, 318. 

of refraction, 332. 
Arc lamp, 264. 

system, 265. 
Armature, 251. 

drum, 260. 

Dynamo, 251. 
Artificial ice, 173. 
Atmospheric, electricity, 195. 

pressure, 113. 
Magnitude of, 114. 
Measurement of, 115. 



Atom, 10. 

Axis, principal, 338. 
Secondary', 338. 

Barometer, 114. 

Uses of, 114. 
Batteries, 198, 208. 

Methods of connecting, 209, 210, 211. 

Secondary, 217. 

Storage, 217. 
Use of, 218. 
Beats, 297. 

Frequency of, 297. 
Bell, electric, 242. 
Bichromate cell, 203. 
Block and tackle, 86. 
Boiling, 141. 

Laws of, 142. 

point, 141. 
Boyle's Law, 120. 
Bright-line spectrum, 357. 
Buoyancy, 106. 

Cause of, 107. 
Bunsen photometer, 315. 

Calorie, 151. 
Calorimetry, 150. 
Camera, 343. 
Capillarity, 18. 

Effects of, 19. 

Laws of, 19. 
Capstan, 85. 
Cells, best arrangement of, 212. 

Bichromate, 203. 

Forms of, 202. 

Gravity, 202. 

Leclanche', 203. 

Multiple connection of, 210. 
377 



378 



INDEX 



Cells, multiple-series connection, 211. 

Secondary, 217. 

Voltaic, 197. 

Series connection of, 209. 

Storage, 217. 

Uses of, 204. 
Center of curvature of lens, 335. 

of gravitation, 48. 

of gravity, 54. 

of mass, 48. 
Centigrade thermometer, 130. 
Centrifugal force, 32. 
Centripetal force, 33. 
C.G.S. system, 37. 
Charging by contact, 186. 
Charles, law of, 160. 
Chemical change, 11. 
Chemical effects of currents, 215. 
Chemism, 10. 
Chords, 306. 
Chromatics, 349. 
Circuit, electric, 199. 

Closed, 199. 

Open, 199. 

Shunt, 224. 
Clouds, 140. 
Coefficient of expansion, 158. 

of cubical expansion, 159. 

of friction, 93. 

of linear expansion, 158, 159. 
Coherer, 270. 
Cohesion, 16, 17. 
Coil, induction, 246. 

Primary, 244. 

Ruhmkorff, 247. 
Uses of, 248. 

Secondary, 244. 
Cold storage, 172. 
Collimator, 362. 
Colors, by combinations, .365. 

by absorption and reflection, 366. 

by interference, 366. 

by photography, 367. 

Cause of, 352. 

Complementary, 365. 

Fundamental, 364. 
Combustion, 127. 
Commutator, 252. 
Compass, mariner's, 177. 
Complementary colors, 365. 
Composition of forces, 30. 
Compound machines, 91. 



Compressibility of gases, 121. 
Concave, lenses, 335. 
Focus of, 336. 
mirrors, 324. 
Complete images by, 325. 
Images of points by, 324. 
surfaces, 322. 
Condensation, 140. 

Condensations and rarefactions, 278. 
Condensers, electric, 193, 247, 
Conduction, of electricity, 197. 

of heat, 143. 
Conductors, pointed, 191. 
Conjugate foci, 326. 
Conservation of energy, 175. 
Consonance, 304. 
Constant force, 28. 
acceleration of falling bodies, 56. 
of gravitation, 49. 
Continuous spectrum, 356. 
Contraction of water, 132. 
Convection, 144. 
Applications of, 146. 
Cooling by, 169. 
Convective discharge, 191. 
Convertibility of energy, 79, 175. 
Convex, lenses, 335. 
Focus of, 336. 
mirrors, 328. 
Cooling, by conduction, 168. 
by convection, 169. 
by expansion, 171. 

Theoiy of, 171. 
by radiation, 169. 
Methods of, 168. 
mixtures, 170. 
Coulomb, 207. 
Crests and troughs, 277. 
Crookes tubes, 248. 
Crystalline lens, 341, 342. 
Crystallization, 134. 
Currents, electric, 197, 204. 
Chemical effects of, 215. 
Direction of, 199, 244. 
Effect of resistance on, 223. 
Eifects of, 214. 
Heat effects of, 214. 
Induced, 243. 

Magnetic effects of, 199, 237. 
Mutual action of, 238. 
Test for, 199. 
Ocean, 146. 



INDEX 



379 



Dark-line spectrum, 357. 
Declination, magnetic, 177. 
Degrees, 130. 
Densitv^ 10. 

Optical, 332. 
Dew, 140. 
Dielectrics, 189. 
Difference of potential, 200. 
Diffusion of light, 322. 
Dipping needle, 183. 
Dispersion of light, 350. 

Cause of, 352. 

Order of, 352. 
Dissonance, 304. 
Doppler principle, 364. 
Double-convex lens, images by, 339. 
Drum armature, 260. 
Ductility, 16. 
Dynamo, 251. 

Electromotive force of, 254. 
Dyne, 40. 

Ear, 299. 
Echo, 280. 

Elastic tension of gases, 122. 
Elasticity, 15. 
Electric, attraction, 184. 
bell, 242. 

charge, 184, 190, 1^)4. 
Attraction of, 185. 
Distribution of, 190. 
Kinds of, 184. 
Static, 184. 
condenser, 193, 247. 
current," 197, 204. 
Chemical effects of, 215. 
Effect of resistance on, 223. 
Effects of, 214. 
Induced, 243. 

Magnetic effects of, 199, 237. 
Mutual action of, 238. 
Test for, 199. 
dynamo, 251. 
lamp, arc, 264. 

Incandescent, 261. 
machine, 192. 
motor, 257. 
pressure, 204. 
repulsion, 185. 
waves, 269. 
Electrical measurements, 222. 
Electricity, atmospheric, 195. 



Electricity, chemical effects of, 215. 

Heat effects of, 214. 

Magnetic effects of, 199, 237. 

Static, 184. 

Voltaic, 197. 
Electrodes, 199. 
Electrolj^sis of water, 215. 
Electromagnet, 238. 

Poles of, 239. 
Electromagnetic induction, 243. 
Electromotive force, 204. 

of dynamos, 254. 
Electrophorus, 187. 
Electroplating, 216. 
Electroscope, gold-leaf, 188. 
Electrostatic induction, 186. 
Electrotyping, 216. 
Energy, 74. 

Conservation of, 175. 

Convertibility of, 79, 175. 

Indestructibility of, 80. 

Kinetic, 77. 
Magnitude of, 77. 

Potential, 78. 
Magnitude of, 79. 

Radiant, 149. 

Transformations of, 80. 

Types of, 76. 
Engine, gas, 164. 

Heat, 164. 

Steam, 165. 
Equilibrant force, 32. 
Equilibrium, 53. 

Neutral, 55. 

Stable, 54. 

Unstable, 54. 
Erg, 75. 
Ether, 149. 
Evaporation, 135. 

Effect, of area exposed, 136. 
of heat on, 136. 

of, on plants and animals, 138. 
of pressure on, 137. 
of substance on, 136. 
of water vapor on, 137. 

Laws of, 138. 
Expansion, 129. 

Applications of, 129. 

Coefficient of, 158. 
Cubical, 159. 
Linear, 159. 

Exceptions to law of, 132. 



380 



INDEX 



Expansion, of gases, 159. 

of solids, 159. 
Extension, 13. 

Measurement of, 6. 
Eye, 341. 
Eyepiece, 344. 

Fahrenheit thermometer, 130. 
Fall of potential, 222. 
Falling bodies, 56, 59. 

Acceleration of, 56. 

Effect of mass on, 57. 
Far-sightedness, 342. 
Field magnets, 251, 260. 

Methods of winding, 260. 
Fields, magnetic, 182. 
Fifth, in music, 305. 
Floating bodies, 108. 
Flue-pipes, 293. 
Fluids, 98. 

Transmission of pressure by, 
Foci, of lenses, 336. 

Conjugate, of mirrors, 326. 
of lenses, 336. 
Focus, principal, 324. 
Fog, 140. 
Foot-pound, 74. 
Foot-poundal, 75. 
Force, 26. 

Absolute unit of, 39. 

Buoyant, 107. 

Composition of, 30. 

Constant, 28. 

Centrifugal, 32. 

Centripetal, 33. 

Graphic representation of, 21. 

Impulsive, 28. 

Lines of, 182. 

Molecular, 9, 16. 

Moment of, 184. 

of gravitation, 27, 45. 

of gravity, 27, 51. 

pump, 116. 

Resolution of, 32. 

Units of, 40. 
Fraunhofer lines, 362. 
Freezing, mixtures, 134. 

point, 1.34. 
Frequency, of beats, 297. 

of vibration, 275. 

Range of, 275. 

of wires, 287. 



Frequency (continued). 

of wires, effect of mass on, 287. 
Effect of tension on, 287. 
Friction, 92, 125. 

Cause of, 92. 

Coefficient of, 93. 

Laws of, 93. 
Fundamental, tone, 289. 

units, 36. 

vibration, 288. 
Fusion, 134. 

Latent heat of, 152. 

Laws of, 135. 

G,50. 
g,5S. 

Determination of, 59. 
Galvanometer, 219. 

Astatic, 220. 

D' Arson val, 220. 

Tangent, 219. 
Galvanoscope, 218. 
Gas engines, 164. 
Gases, 10. 

Compressibility of, 120. 

Elastic tension of, 122. 

Expansion of, 10, 159. 

Liquefaction of, 174. 

Mechanics of, 112. 

Measurement of pressure on, 115. 

media for sound, 276. 
Geissler tubes, 248. 
Gram, 7. 
Gravitation, 27, 45. 

Center of, 48. 

Constant of, 49. 

Effect of mass on, 47. 

Effect of distance on, 46. 

Law of, 47. 

Magnitude of, 48. 

Universality of, 45. 
Gravity, 27, 51. 

Acceleration due to, 58. 

cell, 202. 

Center of, 54. 

Direction of, 54. 

Unit of Force, 40. 

Variation in, 51. 

Hail, 140. 
Hardness, 15. 
Harmonics, 304. 



INDEX 



381 



Heat, 125. 

and energy, 174. 

and temperature, 128, 151. 

and work, 162. 

capacity, 154. 
Natural effects of, 154. 

Cause of, 126. 

Change of state caused by, 133. 

Conduction of, 143. 

Convection of, 144. 

due to combustion, 127. 

due to friction, 125. 

due to percussion, 125. 

effects of electric currents, 214. 

engines, 164. 

equivalent of work, 162. 

Expansion due to, 129. 

Mechanical efficiency of, 167. 

Mechanical equivalent of, 167. 

Nature of, 128. 

of fusion, 152. 

of vaporization, 153, 154. 

Production of, 125. 

Radiant, 148. 

relation to work, 167. 

relation to light, 316. 

Sources of, 127. 

Specific, 151. 

Sun as a source of, 127. 

Total amount of, 156. 

Transference of, 143. 

units, 150. 

waves, 310, 355. 
Hertzian waves, 269. 
Holtz machine, 192. 
Horse-power, 75. 
Hot-air heaters, 147. 
Hot-water heaters, 148. 
Human voice, 293. 
Humidity, 139. 

Effect of temperature on, 139. 
Hydraulic press, 101. 
Hydrometer, 110. 

Constant-volume, 111. 
Hydrostatics, 98. 

Ice, artificial, 173. 
Images, 319. 
Cause of, 325. 
Formation of, 319. 
concave mirrors, 324, 325, 327. 
convex mirrors, 328, 330. 



Images {continued). 

Formation of, lenses, 338. 
plane mirrors, 320. 
spherical mirrors, 322. 

Real, 327. 

Virtual, 327. 
Impulsive force, 28. 
Incandescent lamp, 261. 

circuit, 262. 

Three- wire system, 263. 
Inclined plane, 61, 87. 

Law of, 89. 
Indestructibility of matter, 13. 
Index of refraction, 332. 
Induced electric currents, 243. 

Direction of, 244. 
Induction, coils, 246. 

Electromagnetic, 243. 

Electrostatic, 186. 

Magnetic, 178. 

Self, 245. 
Inductive capacity, 189. 
Inertia, 13. 

Instantaneous speed, 23. 
Intensity of illumination, 314. 

Effect of distance on, 314. 
Interference of light-waves, 354. 
Interferometer, 354. 
Interval, musical, 305. 
Iris, 341. 

Joule's equivalent, 162. 

Kilogram, 8. 
Kilogrammeter, 75. 
Kinetic energy, 77. 
Kinetic theory, 9. 

Latent heat, 152. 

of fusion, 152. 
Law, of Boyle, 120. 

of Charles, 160. 

of gravitation, 47. 

of Pascal, 100. 

of thermodynamics, first, 168. 
second, 169. 

of weight, 53. 
Laws, of fusion, 135. 

of motion, 28, 29, 34. 

of refraction, 333. 
Leclanche cell, 203. 
Lens, crystalline, 342. 
Lenses, 335. 



382 



INDEX 



Lenses, center of curvature of, 335. 
Foci of, 336. 
Images by, 338. 
Optical center of, 337. 
Levers, 82. 

Classes of, 82. 
Leyden jar, 194. 
Lifting pump, 116. 
Light, 308. 

Absorption of, 358. 

Analysis of, 351. 

Candle-power of, 315. 

Cause of, 309. 

Diffusion of, 322. 

Dispersion of, 350. 

Emission and absorption of, 359. 

Intensity of, 313. 

Effect of distance on, 314. 
Interference of, 354. 
Nature of, 308. 
Propagation of, 310. 

Direction of, 311. 

Manner of, 310. 
Radiant energy of, 309. 
rays, 318. 

Incident and reflected, 318. 
Reflection of, 317. 

Direction of, 318. 

from curved surfaces, 322. 

Irregular, 322. 

Laws of, 319. 

Regular, 319. 

Total, 347. 
Refraction of, 331. 

Angle of, 332. 

Direction of, 332. 

Index of, 332. 

Laws of, 333. 

Natural applications of, 348. 
Speed of, 315. 

in transparent media, 331. 
Transmission of, 310. 
waves, 310. 

Interference of, 354. 

Length of, 353. 

Measurement of, 354. 
White, composition of, 350. 
Light and heat compared, 316. 
Lightning, 195. 
Lightning rods, 195. 
Lines of force, 182. 
Liquefaction of gases, 174. 



Liquids, 10. 

Pressure of, 103, 104. 

Surface of, at rest, 102. 
Liter, 7. 

Local action, 201. 
Luminous bodies, 308. 

Energy of, 309. 

Machines, 82. 

Compound, 91. 

Simple, 82. 
Magnetic, induction, 178. 

effects of currents, 237. 

fields, 182. 

needles, 177. 

poles, 178. 
effect upon each other, 178. 
Magnets, 177. 

Effect of breaking, 179. 

Electro, 238. 

Permanent, 178. 

Temporary, 178. 
Magnetism, 177. 

Induced, 178. 

Theory of, 179. 
Malleability, 16. 
Mariner's compass, 177. 
Mariotte's law, 122. 
Mass, 8, 11. 

Center of, 48. 

Conservation of, 13. 

Measurement of, 52. 

Units of, 11,42. 
Mathematical pendulum, 64. 
Matter, 6, 8. 

Changes in, 11. 

Properties of, 13. 

Structure of, 8. 
Measurement, electrical, 222. 

of atmospheric pressure, 114. 

of electric currents, 228. 

of mass, 52. 

of potential, 227. 

of resistance, by substitution. 
231. 
with slide-wire bridge, 234. 
with Wheatstone bridge, 232. 

of weight, 52. 
Mechanical efficiency of heat, 167, 
Mechanics, of fluids, 98. 

of gases, 112. 
Melting-point, 134. 



INDEX 



383 



Meter, 7. 

Metric system, 37. 

Michelson's interferometer, 354. 

Microphone, 265. 

Microscope, compound, 344. 

Simple, 343. 
Mirrors, plane, 320. 

Spherical, 322. 
Mist, 140. 

Molecular vibration, 275. 
Molecule, 8. 
Moment of force, 84. 
Momentum, 25. 

unit of, 39. 
Morse alphabet, 240. 
Motion, 21. 

Accelerated, 25. 

Cause of, 26. 

Composition of, 22. 

Direction of, 21. 

Newton's laws of, 28, 29, 34. 

of stars, 363. 

Path of, 21. 

Resolution of, 23. 

Resultant of, 22. 

Uniform, 24. 

Vibratoiy, 274. 
Motor, electric, 257. 
Multiple connection, 210. 
Music, 303, 304. 

notation, 307. 

scale, 306. 

Near-sightedness, 342. 

Needle, dipping, 183. 

Newton's laws of motion, 28, 29, 34. 

Noise, 304. 

Non-luminous bodies, 308. 

Notes, musical, 307. 

Objective, 344. 
Ocean currents, 146. 
Octave, 305. 
Ohm, 206. 
Ohm's Law, 207. 
Old-sightedness, 342. 
Opaque bodies, 311. 
Opera-glass, 345. 
Optical center, 337. 
Optical density, 332. 
Optical lantern, 346. 
Organ pipe, 291. 



Oscillation, point of, 69. 
Overtones, 289. 

Parallel connection, 210. 
Partial vibrations, 288. 
Pascal's law, 100. 

Experimental proof of, 100. 
Pendulum, 63. 

Compound, 63. 

Laws of, 68. 

Length of, 67, 69. 

Mathematical, 64. 

Measuring time with, 70. 

Measuring g with, 72. 

Motion of, (M. 

Period of, 65, 70. 

Physical, 63. 

Point of oscillation of, 69. 

Point of suspension of, 69. 

Seconds, 70. 

Simple, 63. 
Penumbra, 313. 
Percussion, 125. 
Period of vibration of pendulum, 65, 

Effect of amplitude on, Qiy. 

Effect of g on, 67. 

Effect of length on, 67. 

Effect of mass on, 65. 

Equation of, 70. 
Performance of work by heat, 163. 
Permeability, magnetic, 183, 238. 
Perpetual motion, 175. 
Phonograph, 300. 
Photography, colors by, 367. 
Photometry, 314. 
Physical change, 11. 
Physical pendulum, 63. 
Physics, 2. 
Pitch, 286. 

Numerical value of, 286. 
Polarization of cells, 201. 
Poles, magnetic, 178. 

of cells, 198. 
Porosity, 14. 

Potassium-bichromate cell, 203. 
Potential, 192. 

Cause of, 200. 

Difference of, 200. 

energy, 78. 

Fall of, 222. 

Measurement of, 227. 
Pound, 8. 



384 



INDEX 



Poundal, 40. 
Power, horse, 75. 
Pressure, atmospheric, 114. 

Liquid, 103, 104. 
Principal axis, 324. 
Principal focus, 324. 
Principle of Archimedes, 106. 

Experimental proof of, 107. 
Production of heat by work, 162. 
Projection, lantern, 346. 
Proof-plane, 186. 
Propagation of sound, 276. 

Direction of, 280. 
Properties of matter, 13. 
Pulley, 86. 

Law of, 87. 

single, fixed, 86. 
movable, 86. 

System of, 86. 
Pumps, air, 119. 

Force, 116. 

Lifting, 116. 
Push-button, 243. 

Quality of sounds, 288. 

Kadiant energy, 149. 
Radiation of heat, 148. 
Rain, 140. 
Rainbow, 356. 
Rays, 318. 

Incident and reflected, 318. 

X, 251. 
Receiver, telephone, 266. 
Reed pipes, 292. 
Reflection of light, 317. 

Angle of, 318. 

Direction of, 318. 

Law of, 319. 

Regular, 319. 

Total, 347. 
Refraction of light, 331. 

Angle of, 332." 

Cause of, 331. 

Direction of, .332. 

Index of, 332. 

Laws of, 333. 

Natural applications of, ^8. 
Refrangibility, 351. 
Refrigeration, 168. 
Relay, 241. 
Resistance, 205. 



Resistance, box, 229. 

Determination of, 206. 
by substitution, 231. 
with slide-wire bridge, 234. 
with Wheatstone bridge, 232. 

Effect of, 223. 

Electrical, 205. 

External, 208. 

Internal, 208. 

Laws of, 205. 

of air to falling bodies, 57. 

Unit of, 206. 
Resolution of forces, 32. 
Resonance, 291. 
Resultant, magnitude of, 31. 

waves, 296. 
Retina, 341. 
Rheostat, 230. 
Roentgen rays, 249. 
Ruhmkorff coil, 246. 

Uses of, 248. 

Saturation, 139. 
Scale, musical, 306. 

Thermometric, 131. 
Science, 1. 
Sclerotic coat, 341. 
Screw, 89. 

Laws of, 90. 
Secondary, axes, 338. 

batteries, 217. 
Uses of, 218. 
Seconds pendulum, 70. 
Self-induction, 245. 
Self-luminous bodies, 308. 

Energy of, 309. 
Series connection, 209. 
Shadows, 312. 
Shunt circuits, 224. 

Effect of, 226. 
Sight, .340. 
Siphon, 117. 
Sleet, 140. 
Slide-wire bridge, 233. 

Measurement of resistance with, 
234. 
Snow, 140. 
Solar spectrum, 350. 
Solenoid, 237. 
Solids, 10. 

Density of, 10. 
Sonorous, bodies, 274. 



INDEX 



385 



Sonorous, vibrations, 290. 
Sound, 274. 

Cause of, 276. 

Effect of density of medium on, 285. 

Effect of distance on, 285. 

Effect of temperature on speed of, 
281. 

Experimental evidence of, 282. 

Intensity of, 283. 

media, 276. 

Perception of, 281. 

Propagation of, 276. 

Properties of media, 279. 

Quality of, 288. 

Reflection of, 280. 

Simple, 303. 

Speed of, 280. 
Law of, 281. 

Variations in, 283. 
Sound-waves, 278. 

Coincident, 295. 

Energy of, 284. 

Fundamental, 295, 

Graphic representation of, 294. 

Partial, 295. 

Exception of, 299. 

Resultant of, 296. 

vibrations, 294. 
Sounding-boards, 291. 
Specific gravity, 108. 

of solids, 108. 

flask, 109. 
Specific heat, 151. 
Spectra, 350. 

Absorption, 360. 
Analysis by, 361. 

Bright-line, 357. 

Continuous, 356. 

Dark-line, 357. 
Spectroscope, 361. 
Spectrum analysis, 360. 
Speed, 23. 

Average, 24. 

Constant, 24. 

Instantaneous, 23. 

of light, 315. 

of sound, 280. 

Unit of, 37. 
Spherical aberration, 329. 
Spherical mirrors, 322. 
Standard temperatures, 130. 
Stars, motion of, 363. 
2c 



Static electricity, 184. 

Kinds of charges of, 184. 
Steam-engines, 165. 
Storage cells, 217. 

Uses of, 218. 
Strings, vibrating, 287. 

Laws of, 287. 
Structure of matter, 8. 
Sun, 127. 

Surface tension of liquids, 17. 
Surface and volume, 7. 
Sympathetic vibrations, 291. 
Synthesis of light, 351. 

Telegraph, 239. 

alphabet, 240. 

Duplex and quadruplex, 242. 

Relay, 241. 

Simple system, 239. 

Wireless, 269. 
Telephone, 302. 

Acoustic, 302. 

Electric, 302. 

Receiver, 266. 

System, 267. 
Telescope, 345. 

Galilean, 346. 
Temperature, 128. 

Effect on humidity, 139. 

Standard, 130. 
Tenacity, 15. 
Tension, surface, 17. 
Theory, of cooling by expansion, 171. 

of magnetism, 179. 
Thermal, capacity, 154. 

unit, 151. 
Thermodynamics, first law of, 168. 

Second law of, 169. 
Thermometer, 129. 

Centigrade, 131. 

Fahrenheit, 130. 
Third in music, 306. 
Three-wire system, 263. 
Tone, complex, 304. 

Fundamental and overtone, 289. 

Simple, 304. 
Torricelli's experiment, 113. 
Transformers, electric, 255. 
Translucent bodies, 311. 
Transmission of pressure in fluids, 99. 
Transparent bodies, 312. 
Triads, 306. 



386 



INDEX 



Umbra, 313. 
Units, 3G. 

Derived, 37. 

Fundamental, 36. 

Heat, 150. 

of acceleration, 39. 

of momentum, 39. 

of speed, 37. 

Relation between, 42. 

Use of, 38. 

Vaporization, 135. 

Heat of, 153. 

Laws of, 138. 
Velocity, 24. 
Vibrating air-columns, 291. 

Length of, 292. 
Vibrations, amplitude of, QQ, 285. 

Forced, 299. 

Frequency of, 275. 

Fundamental, 288. 

Longitudinal, 279. 

Molecular, 275. 

Partial, 288. 

Range of frequency of, 275. 

Sonorous, 290. 

Sound, 2.^)0. 

Sound-wave, 294. 

Sympathetic, 291. 

Transverse, 279. 
Vibratory motion, 274. 
Vision, 309. 

Range of, 355. 
Voice, human, 293. 
Volt, 205. 



Voltaic cell, 197. 
Voltaic batteries, 198. 

Uses of, 204. 
Voltaic electricity, 197. 
Voltmeter, 228. 

Watt, 207. 
Wave-motion, 277. 
Waves, actinic, 355. 

Electric, 269. 

Graphic representation of, 294. 

Heat, 310, 355. 

Light, 310. 
Length of, 353. 

Sound, 278. 
Wedge, 89. 
Weight, 34. 

Laws of, 53. 

Measurement of, 52. 
Wheatstoue bridge, 231. 

Measurement of resistance by, 232. 
Wheel and axle, 84. 
Wind, 145. 
Wireless telegraphy, 269. 

System, 271. 
Wires, frequency of, 287. 
Work, 74. 

Heat equivalent of, 162. 

units, 74, 75. 

X-rays, 251. 

Yard, 7. 

Zero, absolute, 157. 



A MANUAL OF EXPERIMENTS 



TO ACCOMPANY 



ELEMENTS OF PHYSICS 



A MANUAL OF 



EXPERIMENTS 



TO ACCOMPANY 



ELEMENTS OF PHYSICS 



BY 



ANDREWS AND HOWLAND 



THE MACMILLAN COMPANY 

LONDON: MACMILLAN & CO., Ltd. 
1903 

All rights reserved 



Copyright, 1903, 
By the MACMILLAN COMPANY. 



Set up and electrotyped January, 1903. 



NORWOOD PRESS 

J. S. GUSHING & CO. — BERWICK A SMITH 

NORWOOD, MASS.. U.S.A. 



LABORATORY MANUAL 



PROPERTIES OF MATTER 



Experiment 1 



Inertia. 



I 



Apparatus. — A bag of sand or other weight of 12 or 15 lb. ; a 
small car, and a cord which will a little more than support the 
weight. 

(1) Suspend the weight from some convenient support 
by means of a piece of the cord, and tie a piece of the 
same cord to the under side of the weight, passing it 
through a hole in a shelf or some sup- 
port placed under the weight to catch 
it if it falls (Fig. 1). 

Now take firm hold of the under 
cord and give it a strong, quick jerk 
downward. Try two or three times to 
be sure there is no mistake. Result? 
Now pull slowly and steadily on the 
lower cord. Result? 

(2) Place the car with the weight 
in it on the table; attach a piece of 
the cord to the car, and pull steadily on 
the cord. Result ? Now jerk quickly 
forward on the cord. Result ? 

Set the car in rapid motion, and, holding firmly to the 
cord, attempt to stop it suddenly. Result ? 

(3) What property of matter is illustrated in these 
experiments ? 

Explain the results obtained in each case. 




Fig. 1. 



2 LABORATORY MANUAL 

Experiment 2 
Porosity. 

Apparatus. — A liter flask ; some alcohol, water, and salt. 

(1) Fill the flask with water to a certain mark on the 
neck, and then pour out a definite quantity. A good 
way to measure the quantity poured out is to take a 
smaller flask and fill it to a marked point on the neck. 
Throw this away and fill the small flask to the same point 
with alcohol, and pour this into the larger flask. Does the 
mixture stand at the same level as the water did at first ? 

(2) Again fill the larger flask with water to a marked 
point, and proceed to sift fine salt slowly into it. Does 
the level of the water begin to rise at once ? 

(3) From the foregoing what do you conclude as to 
the structure of the water and alcohol ? What property 
of matter is illustrated here ? 



Experiment 3 
Cohesion. 

Apparatus. — A specific-gravity balance; a glass disk suspended 
so as to hang in a horizontal position; a dish of water, and a dish of 
mercury. 

(1) Suspend the glass disk from one arm of the balance, 
and balance it with sand or shot. Now place the disk 

upon the surface of the water, 
as shown in Fig. 2, and add 
known weights until the glass 
is torn away from the surface 
of the water. 

Examine the surface of the 

glass. Is it wet ? What force 

holds the water on the surface 

of the glass ? What force was 

Fig. 2. overcome in pulling the glass 




PROPERTIES OF MATTER 3 

away ? Which is stronger, cohesion in water or adhesion 

between water and glass ? 

(2) Repeat the experiment with the mercury. Is the 

glass wet with the mercury ? In which case was the more 

weight required to remove the glass ? Which is stronger, 

cohesion in mercury or adhesion between mercury and 

glass ? 

Experiment 4 
Capillarity. 

Apparatus. — Three glass tubes about 1, 2, and 3 mm., respectively, 
in diameter ; strips of glass, clean and oiled ; strips of zinc, scraped 
clean, and strips of oiled zinc ; a dish of water, and one of mercury. 

(1) Place a strip of glass in the water and note the 
surface of the water around the glass. Repeat with the 
oiled glass. Note in each case whether the glass is wet 
when withdrawn. 

(2) Place a strip of the clean zinc in the dish of mer- 
cury and note the surface of the mercury around the zinc. 
Is the zinc wet with the mercury when it is withdrawn ? 
Repeat with the oiled zinc. 

Under what conditions does a liquid rise around a solid 
which is placed in it ? 

(3) Place the tubes in a glass of cold water and note 
the rise in each tube. Measure the rise and record it. 

Now heat the water and repeat. Again measure the 
height of the water in the tubes, and record. What is the 
effect of heat upon capillarity ? 

(4) Place the tubes in the dish of mercury and note 
the results. How does the action differ in the mercury 
and in the water? In which tube do you get the most 
marked results in each case ? 

(5) Write laws covering the results in each of the 
cases. 

Make diagrams showing the conditions in each case. 



4 LABORATORY MANUAL 

MOTION AND FORCE 

Experiment 5 

Composition of Motions. 

Apparatus. — A sheet of blank paper; some tacks or pins; apiece 
of thread about a foot long ; a ruler. 

Lay the paper on a board, and drive a tack or pin in 
one corner of the paper. Tie one end of the thread to the 

tack. Cut a notch in one 



^ 



Fig. 3. 



corner of the ruler, and place 
' the ruler on the edge of the 
paper, as shown in Fig. 3. 
Tie the other end of the 
thread to tlie point of a lead- 
pencil so that the pencil will 
just reach the edge of the paper, as indicated, and place 
the thread in the notch. 

Push the ruler across the paper, keeping it parallel with 
the edge, allowing the thread to pull the pencil along the 
edge of the ruler and mark its own path. 

From the starting point of the pencil draw a line parallel 
with the edge of the paper, indicating the motion of the 
pencil lengthwise with the paper, and from the end of this 
line draw a line parallel with the end of the paper, indi- 
cating the motion across the paper. 

What relation does the path of the pencil bear to these 
other lines ? 

Experiment 6 

Second Law of Motion. 

Apparatus. — A lath, or similar flat piece of wood, having a cross- 
piece near one end with the ends projecting each side of the lath 
about 2 cm. ; two marbles. 



MOTION AND FORCE 



m. 



Nail the lath by one nail to a high shelf so that the cross 
projects beyond the shelf, as indicated in Fig. 4. Place a 
marble on each arm of the cross, 
and strike the other end of the 
lath a quick blow toward the 
wall. The forw^ard marble will 
be driven forward by the lath, 
while the other will be allowed 
to fall. 

Notice whether the two strike the floor at the same 
time. The most accurate way of determining this is to 
notice the sound caused when they strike. 

How does this tend to prove the second law of motion ? 



Fig. 4. 



Experiment 7 

Composition of Forces. 

Apparatus. — Three dynamometers ; 
two or three feet of fine stout twine. 

Arrange the dynamometers as 
indicated in Fig. 5, connecting the 
hooks with the twine, and clamp- 
ing or otherwise fastening the 
rings to the table top. Mark 
the center of the knot ; draw 
the lines B and CO parallel to the 
twine, and mark on them the 
respective readings of the dyna- 
mometers B and C. 

Remove the dynamometer B, 
and shift C so as to pull the knot 
to the same point as before. 

C now is the equilibrant of A 
and the resultant of B and C as they were at first. 




Fig. 5. 



6 LABORATORY MANUAL 

Draw a line I) parallel with the twine attached to (7, 
and record on it the reading of C. Remove the dyna- 
mometers, and draw the lines BO, CO, and BO, of such 
lengths as to represent the relative magnitudes of the 
three forces. Connect the outer ends of OB and OB with 
a straight line. 

How does this last line compare in direction and length 
with the line OCl If the result is not satisfactory, repeat 
carefully. 

What is the force OB with relation to the other forces ? 

^ Experiment 8 

Center of Gravity. 

Apparatus. — A piece of cardboard ; a pin or tack. 

(1) Thrust the pin or tack through one corner of the 
cardboard so that the cardboard will swing freely in a 
vertical position. Evidently the center of gravity will lie 
somewhere below the pin. Draw a vertical line across the 
paper from the pin downward. 

Change the position of the pin to some other corner of 
the cardboard, and repeat. 

Repeat both of the above-mentioned steps, using the 
other side of the cardboard. 

How does the center of gravitj^ seem to compare in 
position with the center of volume, and hence with the 
center of mass ? 

(2) Tear off one corner of the cardboard, and repeat 
the experiment. 

Experiment 9 

Effect of Mass on Falling Bodies. 

Apparatus. — Two pieces of metal, one about ten times as heavy as 
the other. 



MOTION AND FORCE 7 

(1) Drop the two masses simultaneously from a con- 
siderable height. Notice by the sound whether or not 
they strike together. 

(2) Enclose in a large glass tube a few pieces of tissue 
paper and a pebble. Exhaust the air from the tube, and, 
holding it vertically, quickly invert it. Notice whether 
the pebble falls to the lower end as much quicker than the 
paper as it does when the air is not exhausted. Remem- 
ber the air is probably not more than three-fourths 
exhausted. 

Experiment 10 
The Pendulum. 

Apparatus. — A bullet ; a thread over a meter long ; a clamp. 

(1) Make a pendulum by cutting a notch in the bullet 
and closing the notch over one end of the thread. Sus- 
pend the pendulum by pinching the thread with the clamp 
so fastened to some support that the jaws of the clamp 
are downward. Pass the free end of the thread over the 
clamp support, so that the length of the pendulum may be 
readily changed by loosening the clamp jaws and pulling 
down on the loose end of the thread. 

Cause the pendulum to vibrate in a plane at right 
angles to the jaws; count the number of vibrations in a 
minute, and determine the frequency. 

(2) Make another pendulum of the same length, using 
a wooden bob, and determine its frequency. Or, if con- 
venient, cause the two to vibrate side by side. 

AVhat effect does the mass of the bob have on the fre- 
quency ? 

(3) Using the lead pendulum-bob, determine the fre- 
quency with different amplitudes without changing the 
length. 

What effect does the amplitude have on the frequency ? 



8 



LABORATORY MANUAL 



(4) With the same pendulum-bob determine the fre- 
quency with some convenient length, say one meter, and 
then with the length one-fourth as long. 

The longer the time during which the number of vibra- 
tions is counted, the more accurately the frequency will be 
determined. 

Repeat until satisfactory conclusions can be drawn with 
reference to the relation between the length and frequency 
of the pendulum, and tabulate all results as follows : — 



No. OF 

Trial 


Length 


Material 


Frequency 


Amplitude 


1 

2 
3 
4 

5 
6 

7 











MACHINES 

Experiment 11 



The First-class Lever. 

Apparatus. — A pine rod .5x1.5x30 cm., as shown in Fig. 6, 
with a small block glued or nailed to the top and a small wire nail 
thrust through the middle so that the under side of the nail is on a 
level with the upper surface of the bar. A U-shaped piece of zinc or 
sheet iron ; a block of wood 4x6x8 cm. ; and a set of gram or ounce 
weights. 

Place the rod upon the piece of zinc so that it is sup- 
ported by the nail, being sure that the rod itself does not 
touch the support. Balance the rod by means of a wire 
rider placed on the lighter end. 



MACHINES 



9 





iii/ni!iiiiiiiitiiiiii 




MIIIMIIIIIIIini»1IU 


A 


. 


* n 


/w\ 




r\ 







A 



The supporting nail is called the fulcrum (jF) and may 
be replaced by a triangular prism of wood placed under 
the center of the rod. 

(1) By means of a thread suspend a 100-g. weight 6 cm. 
from F. The distance from where TTis suspended to ^is 
called the weight arm (TFi^); and the weight times the 
length of this arm is sometimes called the — moment, 
because it tends to p 

cause rotation in the 
direction opposite to 
that of the hands of a 
clock. Now suspend 
a 50-g. weight from 
the other arm of the lever, and move it to a position so 
that the lever is in equilibrium. The distance from where 
P is suspended to F is called the force arm (P^), and the 
product of P times the arm PP is called the + moment, 
because it tends to cause rotation in the direction of the 
hands of a clock. When the lever is balanced, how do 
the + and — moments compare ? 

Ounce weights may be used instead of the gram 
weights. 

(2) Repeat with several different combinations of 
weights and lengths of arms and record as follows : — 



Fig. 6. 



Trial 
1 

2 
3 
4 

5 
6 

7 



Weight 



WF 



Prod. 



Force 



PF 



Prod. 



10 LABORATORY MANUAL 

Experiment 12 

The Second-class Lever. 

Apparatus. — A pine rod .5 x 1.5 x 30 cm.; a triangular prism of 
hard wood ; a dynamometer registering grams or ounces, "and several 
weights, varying from 6 to 32 oz. or from 200 to 2000 g. The first- 
class lever used in Experiment 11, with a set of weights, may be sub- 
stituted for the dynamometer. 

(1) Arrange apparatus as shown in Fig. 7, with one 
end of the bar resting on the prism, the fulcrum being 

just 1 cm. from the end, 
the other end of the rod 
extending out over the end 
of the table ; or the prism 
i^ being set upon a block or 
box to admit of the suspen- 
sion of the weight. Place 
a loop of strong thread 
1 cm. from the other end, 
and support the bar by 
means of the balance. If 
the weight of the rod is sufhcient to draw the pointer 
of the balance down any, take the reading carefully, and 
subtract this, which is called the zero reading, from the 
subsequent readings of the balances. 

Suspend a 200-g. weight 11 cm. from F, and take the 
reading. The force arm (Pi^) will be 28, and the weight 
arm ( WF^ will be the distance from the place of sus- 
pension of the weight to the fulcrum. 

Compare the products of the force times the length of 
the force arm with the product of the weight times the 
length of the weight arm. 

(2) Make at least four trials with different weights and 
different lengths of arms, and record as in Experiment 11. 




Fig. 7. 



MACHINES 



11 



(3) If the other arrangement of apparatus is used, 
arrange as in Fig. 8, suspending the end of FF by a loop 
of thread from the 



jm 



mimi 



s 



Fig. 8. 



end of the first-class u r i 1 1 1 i^i i i -^rr^ 

lever, so that the 
force may be ap- 
plied to F by plac- 
ing weights at F'. 
Balance the appa- 
ratus by placing 
any convenient weight upon the arm F'F^. Place a 
10-g. weight at F' and see where a 20-g. weight must be 
placed upon FF to balance it. 

If two weights are placed at different points upon either 
arm, the sum of their moments is the moment for that arm. 

Make the trials necessary to fill the following table. 
Remember that the lever F' X does not enter into the 
calculations, but that the force applied downward at F' 
is applied upward unchanged at F. 



Trial 


P 


PF 


Moment 


W 


WF 


Moment 


1 


10 


28 




20 






2 


10 


28 




50 






3 




28 




20 
10 


5 

8 




4 


5 


26 




10 
5 






5 















12 



LABORATORY MANUAL 



Experiment 13 



W 



I 



\/ 



Fig. 9. 



The Third-class Lever. 
Apparatus. — As in Experiment 12. 

(1) As in Experiment 12, either of two arrangements of 
apparatus may be used. First, the prism of wood may be 
placed under the end of a piece of board which is raised 

o above the table or under the 

projecting edge of the table 
itself. Hook the spring bal- 
^ ance into a loop of cord and 
suspend it from a ringstand 
or other convenient support, 
as shown in Fig. 9. Take 
the reading of the balance without any load, and subtract 
this zero reading from each of the subsequent readings 
of the balance. 

See that the end of the lever rests against the edge of 
the prism exactly at the first centimeter mark from the 
end; place the loop 7 cm. from F; hang a 20-g. weight 
1 cm. from the other end, and take the reading of the 
balance. Compare the products of the force times the 
length of its arm (P^) and the weight times the length of 
its arm (TF-F). ^ p, 

(2) The second ar- 
rangement of apparatus 
is shown in Fig. 10. 
A wire nail is driven 
through the lever WF 
just 1 cm. from the 
end, and the ends of the nail hooked under two screw 
hooks which are placed a little more than the width of 
the lever apart. Over this is placed the first-class lever 
used before, the two being connected as before by a 



S3 



oj 



^ 



Fig. 10. 



MACHINES 



13 



loop of cord. Balance the apparatus by placing on, or 
suspending from, P' F' any convenient weight. The 
force is applied by placing the required weight at P' and 
making P' F' equal to XF' ; then the force applied upward 
at P will be equal to P\ so that the lever XP' does not 
enter into the calculations. As before, make PF 7 cm. 
and place 20 g. 28 cm. from F. What force must be ap- 
plied at P' to balance it ? 

(3) Make several trials with different weights and 
lengths of arms, and record as shown in the following 
table : — 



Trial 


p 


PF 


Moment 


W 


WF 


Moment 


1 




7 




20 


28 




2 














3 














4 














5 















From the foregoing experiments what relation do you 
find between weight and weight arm and force and force 
arm ? State in the form of a law. 



Experiment 14 

The Single Fixed Pulley. 

Apparatus. — A single-grooved pulley ; a dynamometer ; a cord ; and 
a 500-g. or a 1-lb. weight. 

(1) Arrange the apparatus as shown in Fig. 11, apply- 
ing the dynamometer at P. As the balance is inverted it 
will read twice the weight of the draw-bar and hook less 
than it should, and the readings must be corrected for this. 



14 



LABORATORY MANUAL 




Draw the weight slowly up, and, while it is in motion, 
take the reading of the balance ; then, while lowering the 
weight at the same rate, again take the read- 
ing. The up reading will be the force required 
to support the weight plus the friction, while 
the doAvn reading will be the force minus the 
friction ; the average, corrected for the zero 
reading, will be the correct force. 

(2) How does the force compare with the 
weight ? Measure the distance that the weight 
is raised when the power is pulled down a 
certain distance. How do these distances 
compare ? What, then, is the advantage of 
the single fixed pulley ? 



t B 



Fig. 11. 



(S) 


Make several trials, and recoi 


d as follows ; — 




Trial 


"Weight 


Force Up 


Force Down 


Average 


Corrected 


1 

2 
3 















Experiment 15 

The Single Movable Pulley. 

Apparatus. — Same as in Experiment 14, and a 
loose pulley. 

(1) Arrange the apparatus as shown in 
Fig. 12 so that the end of the cord is 
attached to a rigid support, the pulley 
being suspended in the loop of the cord, 
the weight being suspended from the loose 
pulley, and the force being applied at P. 

Carefully weigh the pulley and weight 
together and call this W. 




MACHINES 



15 



There are now how many parts of the cord supporting 
the weight? Each part of the cord, then, will support 
what part of the weight ? 

As in Experiment 14, take the reading of the balance 
while the weight is being raised, and then while it is being 
lowered, and the mean will be the required force. 

(2) Try with several different weights. 

Record as follows : — 



Trial 


"Weight 


P. Up 


P. Down 


Average 


No. OF Parts 
OF Cord 


Prod, ok 
Last Two 


1 

2 















(3) Also measure the distance TT rises and call it WB^ 
and the distance P rises and call it PD. Compare, in a 
table, the product of P and Pi), and of W and WD : — 



Trial 


P 


PD 


Prod. 


W 


WD 


Prod. 


1 

2 















Experiment 16 

The Block and Tackle. 

Apparatus. — Two blocks containing two or 
more pulleys, with cord and balance arranged as 
in Fig. 13 a, and several weights varying from 
1 to 5 kg. or 2 to 10 lb. 

(1) Suspend the apparatus from some 
convenient support so that the end of the 
cord is attached to the stationary block, 
as shown in the figure. How many parts 
of the cord are there now supporting the 
weight ? 




16 LABORATORY MANUAL 

Take the up and down reading of the balance represent- 
ing the force as before, and also measure the distance the 
force moves in raising the weight one linear unit, as in 
the preceding experiment, 

(2) Now reverse the apparatus so that the end of the 
cord is attached to the movable block as shown in Fig. 14 5, 
and note that the number of parts of the cord supporting 
the weight is increased by one. 

Again take the up and down reading of the balance, 
and the relative distance travelled by the force and the 
weight, and tabulate results. 

(3) From the foregoing state the law governing the rela- 
tion between force and weight when a set of pulleys with 
a continuous cord is used. 

What is the influence of the place of attachment of the 
end of the cord upon the number of supporting cords 
and the force required to support a given weight ? 

Experiment 17 

The Inclined Plane. 

Apparatus. — A board 8 or 10 in. wide and 3 ft. long ; a car or iron 
roller weighing about 5 lb. ; a dynamometer; and some support to 
hold up one end of the board. 

(1) Arrange the apparatus as shown in Fig. 14, and 
from the point a where the board rests upon the table 

measure 80 or 
100 cm. to b. 
Raise the end 
of the board so 
that the per- 
I pendicular dis- 
tance cb will 
be about one- 
fourth ab. Hook the balance to the car, and, holding the 




Fig. 14. 



MECHANICS OF FLUIDS 



17 



balance parallel to the surface of the plane, draw the car 
up the plane. While the car is in motion, take the read- 
ing of the balance. Then let the car roll down the plane, 
and, while it is moving at as nearly as possible the same 
rate as before, take the reading of the balance. The 
average of these two readings would be the force required 
to support the weight if the car were frictionless. 

Calling the perpendicular distance cb that the car rises 
WD^ and the distance ab that the force moves to raise 
it this height PD, compare the product of P and Pi>, 
and of W and WD. 

(2) Make at least three trials with the board at differ- 
ent angles, and record the results in tabular form as fol- 
lows : — 



Trial 


Force 
Up 


Force 
Down 


Mean 


PB or ab 


Prod, of 
Last Two 


Weight 


WD or 

cb 


Prodttot 


1 

2 
3 



















- Three glass tubes 3 or 4 mm. in diameter, bent as 
15 ; a hydrometer jar and some mer- 



MECHANICS OF FLUIDS 

Experiment 18 
Liquid Pressure. 

Apparatus. - 

shown in Fig 
cury. 

Place some mercury in the upper bend 
of each of the tubes so that it stands at the 
same level in all three. The tubes should 
be of such a length that when they are hung 
on the edge of the glass jar the mercury 
will be at the same level in all and the 
openings at the lower ends will all be at the same level. 



ly 



w 



Fig. 15. 



lyj 



18 LABORATORY MANUAL 

Lower the tubes all together into the water and note 
the effect upon the mercury. 

The air in the tubes transmits the pressure to the mer- 
cury, and of course the greater the difference of level 
between the two surfaces of a given column of mercury, 
the greater the pressure indicated. 

What seems to be the effect of increased depth upon 
the pressure ? 

The tubes are so bent that the water pressure is applied 
at the same depth in three directions, downward, upward, 
and laterally. What seems to be true of the magnitude 
of the pressure in all directions at a given depth ? The 
magnitude of liquid pressure upon a given surface depends 
upon what ? 

Experiment 19 

Measurement of Upward Pressure upon a Submerged 
Surface. 

Apparatus. — A battery jar of water; an argand lamp chimney or a 
1-in. glass tube with a ground end ; and a piece of cardboard. 

Place the piece of cardboard over the end of the tube 
and lower it into the water, moving it around to see that 
the cardboard is held firmly in place. Now pour water 
slowly into the tube until it is nearly on a level with the 
water in the jar. 

Move the tube around slowly and raise and lower it at 
the same time, and note the relation between the water 
level inside and out of the tube when the force ceases 
which holds the cardboard in place. 

The upward pressure of the water on the surface of the 
cardboard is then equal to the downward pressure of the 
water in the tube on the cardboard. Hence the upward 
pressure on the cardboard is equal to the weight of a 
column of water of what dimensions ? 



MECHANICS OF FLUIDS 



19 



Experiment 20 

Determination of the Downward Pressure of a Liquid 
upon the Bottom of the Containing Vessel. 

Apparatus, — As shown in Fig. 16, which consists of several vessels 
of different sizes and shaj^es, but all having uiovable bottoms of the 
same size, which are held iu place by means of weights upon the scale 
pan. 

Place the vessel 
with the straight 
sides in position and 
attach the bottom to 
one arm of the scale 
beam, and in the pan 
attached to the other 
end of the beam 
place any convenient 
weight. 

Slowly pour water 
into the vessel until its weight pushes the bottom down 
and the water begins to run out. Measure the depth 
of the water that will be retained without any material 
leakage, and record. 

It is well to use the vessel with the straight sides first, 
as then we know that the pressure upon the bottom is the 
weight of a column of the liquid, the base of which is 
the bottom of the vessel and the altitude the depth of 
the water. 

Replace this vessel with each of the others in turn and 
measure as in the first trial. 

What do you find to be true of the depth of the water 
in each case ? Does the size or shape of the vessel influence 
the pressure upon the bottom when the depth remains the 
same and there is no change in the area of the bottom ? 




Fig. 16. 



20 LABORATORY MANUAL 

Write a rule or law for the downward pressure of a 
liquid upon the bottom of containing vessels. 

buoyancy and specific gravity 

Experiment 21 
Floating Bodies. 

Apparatus. — A pine stick exactly a centimeter square and 20 or 30 
cm. long, with one end weighted, by boring a hole and filling it with 
lead, so that it will float upright in the water. The stick should be 
dipped in hot paraffin to make it impervious to water, after it has 
been marked off in centimeters, beginning at the heavy end. 

Weigh the stick carefully, and then place it in a deep 
vessel of water and note carefully how much of its length 
is under water. 

If a cubic centimeter of water weighs one gram, what 
weight of water is displaced by the floating body ? How 
does this compare with the weight of the body ? 

Write your conclusion as to the weight of a liquid dis- 
placed by a body floating in it. 

Experiment 22 

Principle of Archimedes, or the Loss of Weight of a Solid 
submerged in a Liquid. 

Apparatus. — A cylindrical brass cup fitted with a brass plug that 
exactly fills it ; or a small, wide-mouthed, glass-stoppered bottle and a 
^— - specific-gravity balance. 

/\ First Method. — Arrange the apparatus as 

U'^ shown in Fig. 17 with the plug hanging from 

S^ the bottom of the cup. Balance the scales by 

IP placing weights in the right-hand pan. Then 

^md place the plug in a glass of water so that it is 

Biro entirely submerged, but do not allow the bottom 

Fig. 17. of the cup to touch the water. Is the balance 



BUOYANCY AND SPECIFIC GRAVITY 21 

now in equilibrium ? Now pour water into the cup until 
equilibrium is again restored. How does the volume of 
the water poured in compare with the volume of the plug ? 

Second Method. — Fill the wide-mouthed bottle with 
water and press the stopper in with a twisting motion as 
far as it will go, being sure that there are no air bubbles 
in the bottle. Place the bottle on the scale pan, and with 
it a piece of iron or brass which will go into the bottle. 
Weigh the two together, and then place the weight in the 
bottle and cork as before. Wipe off the water that over- 
flows, and again weigh. The difference of these two 
weights will be the weight of what bulk of water ? 

Now dry the mass of metal and weigh it in air ; then 
suspend' it in a glass of water and again weigh. How 
does the difference of these two weights compare with the 
difference in the other case ? 

From the foregoing what do you conclude as to the loss 
of weight of a solid when submerged in a liquid lighter 
than itself ? 

Experiment 23 

To determine the Specific Gravity of a Solid Heavier 
than Water. 

Apparatus. — Specific-gravity balance ; several solids heavier than 
water ; and a glass of water. 

(1) Weigh the solid, the specific gravity of which is to 
be determined; then suspend it from the hook on the under 
side of the scale pan so it will be immersed in the glass of 
water, and again weigh. The difference of these two 
weights will be the weight of what volume of water ? 

Divide the weight of the solid in air by its loss of weight in 
water and the result will be the specific gravity of the solid. 

(2) Determine the specific gravity of several common 
solids, as iron, copper, lead, zinc, and marble. 



22 LABORATORY MANUAL 

Experiment 24 

To determine the Specific Gravity of a Solid Lighter 
than Water. 

Apparatus. — Balance as in the last experiment; piece of cork or 
paraffined pine ; a sinker heavy enough to sink the light body. 

Weigh the pine in the air. Weigh the sinker in air 
and in water ; the difference will be the weight of the 
water displaced by the sinker. Tie the pine and sinker 
together, and weigh the combined mass in air and then in 
water; the difference will be the weight of water displaced 
by the combined mass. Subtract the Aveight lost by the 
sinker when weighed in water from the loss of the com- 
bined mass, and the difference will be the weight of the 
water displaced by the pine alone. Divide the weight of 
the pine in the air by this difference, and the result will be 
the specific gravity of the pine, which of course will be less 
than one. 

Experiment 25 
The Barometer. 

Apparatus. — A glass tube about 1 m. long and 3 mm. in diameter, 
closed at one end, and a dish of mercury. 

Fill the tube with mercury, and remove the air bubbles 
which cling to the inside of the tube with a piece of 
cotton-covered wire. 

Place the finger over the end of the tube, being sure 
that there is no air in the tube, and invert it in the dish 
of mercury so that the open end of the tube is immersed 
in the mercury. Remove the finger, and the mercury will 
drop to a certain level. What force sustains the mercury 
in the tube ? 

Measure the height of the column of mercury above the 
level of the mercury in the dish. 



BUOYANCY AND SPECIFIC GRAVITY 



23 



Supposing the tube to have a cross section of one square 
centimeter, and that mercury is 13.6 times as heavy as 
water, find the weight of the mercury column, and thus 
the downward pressure of the atmosphere per square cen^ 
timeter on the surface of the dish of mercury. 



Experiment 26 

Boyle*s Law, or the Effect of Pressure upon the Volume 
of a Gas. 

Apparatus. — A glass tube, bent as shown in Fig. 18, with its 
longer arm at least a meter long and its shorter arm 12 or 15 cm., the 
latter being sealed. The tube should be mounted upon 
a board with a base, so it will stand upright, and 
should have a scale fastened to each arm. The short 
scale should read down from the top of the short tube, 
the mark being on a level with the top of the tube. 
The scale which is placed by the long arm will be much 
more convenient if it is mounted in such a way that 
it can be moved up and down easily, so that the 
mark may be placed on a level with the mercury in the 
short tube, and thus the height of the mercury in the 
long arm easily and directly read. 

(1) Put a little mercury into the tube and 
manipulate it so that it stands at the same 
level in both arms of the tube. We know 
then that the air in the short tube is under 
the same pressure as the outside air, that is, 
one atmosphere. 

Record the length of the air column in C, and pour mer- 
cury into AB until it stands at a height above the level 
of the mercury in equal to one-half the height of the 
barometer column when the experiment is performed. 
What is now the length of the air column ? If the first 
pressure upon the air in C was one atmosphere, what is 
the pressure that it now sustains? 



u 



Fig. 18. 



24 LABOBATORY MANUAL 

Now fill AB so that the height of the mercury above 
the level of the mercury in is equal to the height of the 
barometer column. What is now the pressure in atmos- 
pheres upon the air in C^ ? What is its volume now ? 

(2) Calling the first volume of air ab^ the second a'b\ 
and so on, make proportions showing the relation between 
volumes and pressures, writing the pressures in atmos- 
pheres, as ab : a'b' = 2:1, which represents the conditions 
in the last case. 

Try several cases with the mercury at different heights, 
and write a proportion for each trial. 

Write the law for the effect of pressure upon the volume 
of a quantity of gas under different pressure. This is 
called Boyle's Law. 

Experiment 27 

The Lifting Pump. 

Secure a glass model of the lifting or suction pump, 
and, working it slowly and carefully, watch the action of 
the valves. Then make drawings showing the condition 
of the valves during the up and down strokes, and explain 
the action of the pump. 

HEAT 

Experiment 28 

Production of Heat. 

Apparatus. — A button ; a hammer and an anvil ; a piece of heavy 
wire or iron rod ; a glass flask or bottle ; a thermometer ; 4 or 5 cm.^ 
of mercury ; a bicycle pump. 

(1) Rub the button briskly on a piece of cloth, and 
notice the increased warmth. 

Pound the iron rod on the anvil, and touch the end. 

Pour the flask about half full of water, and wrap the 
flask in several folds of paper. Take accurately the tem- 



HEAT 25 

perature of the water, and shake the flask vigorously for 
some time. Take the temperature again. 

Mercury is more effective than water in this experiment, 
but care must be used to avoid breaking the flask if the 
glass is thin. 

(2) Force air for some time vigorously with the bicycle 
pump into a tire or other apparatus, and notice the in- 
creased temperature of the cylinder of the pump. 

Draw conclusions as to the cause of the increased warmth 
in the various cases. 

Experiment 29 

Freezing-point of Water. 

Apparatus. — A tumbler ; some snow or pounded ice ; a ther- 
mometer. 

The purpose of this experiment is to determine whether 
the freezing-point indicated by the thermometer used is 
correct. 

Fill the tumbler full of snugly packed snow, and thrust 
into it the thermometer, keeping it so the mercury column 
appears just above the snow ; but do not let the lower end 
of the thermometer touch the bottom of the tumbler. 
Let the outfit stand until the top of the mercury remains 
stationary for at least several minutes, keeping the snow 
packed around the thermometer. 

The height of the column should then indicate the 
freezing-point of water. 

Notice the amount of error of the thermometer indica- 
tion, if any, and whether it reads too much or too little. 

Experiment 30 

Boiling-point of Water. 

Apparatus. — The thermometer used in Experiment 29 ; a Florence 
flask with a capacity of about 500 cm.^ ; a Bunsen burner. 



26 LABORATORY MANUAL 

(1) Fill the flask about one-third full of water, distilled, 
if convenient ; wipe the flask dry on the outside to avoid 
breaking, and heat the water to boiling. 

Suspend in the neck of the flask the thermometer, so 
that the lower end is just above the water. Allow the 
water to boil freely, until the top of the mercury column 
remains at rest for several minutes. The height of the 
column should then indicate the boiling-point at the ex- 
isting atmospheric pressure. 

Read the barometer. The boiling-point should be 100° 
if the barometer indicates 760 mm. Or it should be 
approximately as many degrees above or below 100° as 
the number of millimeters, divided by 27, which the 
barometer column is above or below 760 mm. 

Determine what the boiling-point should be at the 
present pressure, and the difference between this and the 
point indicated by the mercury column of the thermometer 
in the experiment will be the error of the thermometer. 

(2) From this error and the error found in Experi- 
ment 29, determine the error at 50°. 

Experiment 31 
Conduction of Heat 

Apparatus. — Several small bars or wires of iron, copper, alumin- 
ium, and other metals ; a Bunsen burner; along test-tube; a ther- 
mometer. 

(1) Place one end of each wire in the Bunsen flame, 
keeping the wires separated. Notice by touching the 
wires, a few inches from the flame, the relative conduc- 
tivities of the metals. 

This test is only approximate, as the specific heats of 
the metals affect the rate at which they are warmed. 

If possible, test in some similar manner the conductivi- 



HEAT 27 

ties of other solids, such as wood, asbestos, slate, or clay 
(clay-pipe). 

(2) Fill the test-tube nearly full of water, and take the 
temperature of the water. Then heat the upper part of 
the water, taking care not to allow the flame to come in 
contact with the glass above the water surface. 

When the upper portion of the water boils, thrust the 
thermometer quickly to the bottom of the tube and take 
the temperature of the lower part of the water. 

What is your conclusion as to the power of water to 
conduct heat ? 

Experiment 32 

Specific Heat of a Metal. 

Apparatus. — A metal weighing several hundred grams ; a calorim- 
eter; a thermometer ; a Bunsen burner. 

The purpose of this experiment is to determine the 
specific heat of the metal by heating it to about 100° and 
then cooling it in water, noticing the increase in tempera- 
ture of the water. 

Suspend the metal in boiling water until it has ac- 
quired the temperature of the water ; determine the tem- 
perature of the water by means of the barometer or a 
thermometer. 

Weigh the calorimeter ; fill it about two-thirds full of 
distilled water, and weigh again. Determine thus the 
mass of the water and also find its temperature, which 
should be lower than the temperature of the room. 

Remove the metal quickly from the boiling water, shak- 
ing off as much water as possible, and suspend it in the 
distilled water so that it will not touch the sides or the 
bottom of the calorimeter. 

Stir the distilled water with the thermometer until its 
temperature ceases to rise, and record the temperature. 



28 LABORATORY MANUAL 

From the temperature readings determine the fall in 
temperature of the metal and the rise in temperature of 
the distilled water. 

The mass of the water times its rise would be the num- 
ber of calories imparted to it and hence lost by the metal. 

From the results determine the specific heat of the 
metal, which is the number of calories required to raise 
the temperature of one gram of the metal one degree. 

The result will be only approximate because of the heat 
imparted to the calorimeter and because of other unavoid- 
able errors. 

Experiment 33 
Cooling Mixture. 

Apparatus. — Some ice and salt. 

Place side by side two pieces of ice of about equal 
weights, and on one piece sprinkle some salt. Notice 
which piece melts faster. 

Mix intimately a handful of salt and two or three times 
as much snow or pounded ice. After a few minutes take 
the temperature of the mixture. 

MAGNETISM 

Experiment 34 
Magnetic and Non-magnetic Substances. 

Apparatus. — Iron filings, brass chips, sawdust, pieces of a watch- 
spring or knitting-needle, and a bar magnet. 

Place some of the mixture of filings, sawdust, etc., on a 
paper or in a small box, and stir it with a piece of the 
watch-spring, or knitting-needle, two or three inches long. 
Do you get any results? 

Now draw the piece of spring from end to end several 
times, and always in the same direction, across one end of 
the magnet. 



MAGNETISM 29 

Again stir the mixture. Result? Examine carefully 
and see if all of the materials in the mixture are picked 
up, and if not, which ones are attracted. 

Substances which are attracted by a magnet or become 
magnetized are called magnetic substances, and those which 
do not are called non-magnetic. 

Experiment 35 

The Magnetic Needle and Magnetic Poles. 

Apparatus. — The magnet of Experiment 34 with the addition of 
a paper or wire stirrup suspended by means of a narrow ribbon 
(Fig. 19) ; and a second magnet. 

(1) Suspend one of the magnets in the 
stirrup and watch to see if it comes to rest 
in any particular position. Change its posi- ^ 
tion several times to be sure, and see that 



the second magnet is not near it. p^^ ^g 

The end which points to the north we 
call the north-seeking pole, or simply the north pole, and 
the opposite end the south pole. 

The mariner's compass is simply a small bar magnet 
pivoted so that it can rotate freely in a horizontal plane. 

(2) The poles of magnets used in laboratories are 
usually marked N and S. Bring the north pole of the 
second magnet near the north pole of the suspended mag- 
net. Result? Bring the south pole of the second magnet 
near the south pole of the suspended magnet. Result? 

Bring the north pole of the second magnet near the 
south pole of the suspended magnet. Result? Repeat 
with the opposite poles. Result? 

What do you conclude as to the effect of like and oppo- 
site poles upon each other? State your conclusion in the 
form of a law. 




30 LABORATORY MANUAL 

Experiment 36 
Magnetic Induction. 

Apparatus. — Bar magnet, small bar of soft iron or a wrought nail ; 
a pocket compass, or a magnetoscope (Fig. 20) made by hanging a 
short piece of magnetized watch-spring or knitting-needle in a small 

Florence flask by means of a piece of untwisted silk fiber ; 

some fine iron filings. 

(1) Dip the soft iron bar in the filings ; if 
it does not pick up any, it is free from mag- 
netism. Then bring first one end and then the 
other near the poles of the magnetoscope or an 
ordinary compass needle. If the bar is entirely 
free from magnetism, either end will attract either pole of 
the needle. 

Hold one end of the bar near, but not touching, the 
north pole of the magnet, and bring the other end down 
to the iron filings. What happens? Holding the bar 
still, slowly remove the magnet. What happens? Test 
the end of the bar for polarity, while the other end is held 
near the magnet, by bringing it near the north pole of the 
compass. What happens? 

Make a diagram showing the arrangement of poles in 
the magnet and soft iron bar. 

(2) Repeat, using an unmagnetized piece of steel in 
place of the soft iron. How does its induced strength 
compare with the induced strength of the soft iron? 
Which makes the best induced or temporary magnet? 

(3) Stroke first the soft iron and then the piece of 
steel on one pole of the magnet as you did the watch- 
spring in Experiment 34, and test each for magnetic 
strength by dipping in the iron filings or bring it near 
the compass. 

Which material makes the best permanent magnet? 



MAGNETISM 81 

Experiment 37 



Magnetic Fields. 



Apparatus. — Two bar magnets of equal strength ; fine iron filings ; 
a salt shaker; two rulers of about the same thickness as the mag- 
nets ; and a piece of cardboard or, better, several pieces of blue -print 
paper. 

(1) Lay one of the magnets on the table with a ruler a 
few inches distant on either side, and lay the cardboard 
over them with the magnet under the middle of the paper. 
Sprinkle filings evenly over the cardboard, and jar slightly 
to help their arrangement ; then make a diagram to show 
the direction and arrangement of the lines of force which 
will be mapped by the filings. 

(2) Repeat with the blue-print paper, placing the outfit 
on a window ledge or other place where the light is strong ; 
sprinkle the filings on as quickly as possible, tap into place, 
and let it stand until the exposed paper has turned quite 
dark. Pour the filings off, and wash the paper in running 
water until all the free color is washed out. Spread on a 
pane of glass or drawing-board to dry. 

(3) Place the opposite poles of the two magnets about 
an inch apart with the magnets in line, and, laying the 
paper with its center over the space between the poles, re- 
peat as with the single magnet. 

(4) Repeat with like poles toward each other. 

(5) Repeat with the two magnets laid parallel, with 
opposite poles in the same direction, and then with like 
poles in the opposite direction, with the magnets about an 
inch and a half apart. 

(6) How do lines of force from opposite poles act toward 
each other ? from like poles ? Do you see in this experi- 
ment any reason for or proof of the law governing the 
action of magnetic poles upon each other? 



32 LABORATORY MANUAL 

STATIC ELECTRICITY 

Experiment 38 

Electrification by Friction. 

Apparatus. — Glass and vulcanite or hard rubber rods; pieces of 
silk and flannel, and bits of paper, sawdust, etc. 

Cold, dry weather is desirable for experiments in static 
electricity. 

Bring the glass rod near the light substances. Do you 
get any results ? Now rub the rod briskly with the silk, 
and again bring it near. What is now the result ? Re- 
peat with the vulcanite rod. Result ? 

What evidence do you have that there is some change in 
the condition of the rods when they are rubbed ? 

This condition we call electrification, or we say that the 
rod is charged with static electricity. 

Experiment 39 
To determine the Nature of Static Charges of Electricity. 

Apparatus. — Rods as before ; silk and flannel and a stirrup of paper 
or wire suspended by means of silk fiber or narrow silk ribbon 
(Fig. 21). 

Rub the glass rod with the silk and place 
it in the stirrup, being careful not to touch 
the rubbed end. Then rub a vulcanite rod 
and bring the rubbed end near the rubbed 



Fig. 21. ®^^^ ^^ ^^® glass rod. Result ? 

Now rub another glass rod and bring it 
near the suspended one. Result ? Repeat with two vul- 
canite rods. Result ? 

What do you conclude as to the nature of the charges 
produced by rubbing the different rods ? The charge pro- 



STATIC ELECTRICITY 33 

duced upon the glass wlien rubbed with silk we call, for 
convenience, a positive or + charge, and that generated 
upon the vulcanite rod when rubbed with flannel a nega- 
tive or — charge. 

What did the experiment prove in regard to the action 
of like and unlike charges upon each other ? State con- 
clusion in the form of a law. 

Experiment 40 

The Gold-leaf Electroscope. 

Apparatus. — A gold-leaf electroscope, which consists of a wire with 
a ball, covered with metal or tin foil, at one end. The other end should 
be bent at right angles, with two narrow leaves of gold or Dutch leaf 
attached to it. The wire should be put through a rubber stopper or 
small glass tube in a cork, and the whole placed in a flask, as shown in 
Fig. 22, to protect the leaves. Glass and rubber rods, and silk and 
flannel pads. 

(1) Rub the glass rod and, holding it 
high above the electroscope, bring it slowly 
down, watching the leaves all the time. 
What happens? The rod should not be 
brought nearer than 6 or 8 in. from the ball. 

In this case the supposed condition of the 
electroscope is shown in Fig. 22, the + and 
— signs representing the charges. As like 
charges repel, it will readily be seen why 
the leaves separate. 

Touch the ball lightly with the glass rod. What hap- 
pens ? Do the leaves drop together when the rod is 
removed ? The instrument is now charged with a + 
charge. Bring a charged rubber rod slowly down over 
the ball, and note carefully the result. What happens ? 

(2) Bring the charged glass rod near the ball, and, 
while holding it in position, touch the ball with the finger, 




34 LABORATORY MANUAL 

What happens ? Remove first the finger and then the 
rod. What happens ? Now bring a vulcanite rod slowly 
near. What happens ? Bring the glass rod near. What 
happens ? In each of these last cases the rod must be 
brought slowly near from a considerable distance and the 
first action recorded. 

If after touching the ball we had a + charge, and bring- 
ing the — rod near caused the leaves to fall together, what 
must have been the nature of the charge in the last case ? 

The first process was charging by contact or conduction, 
and the charge imparted was like the charging rod. In 
the second case the method is called charging by induc- 
tion. How does the induced charge compare with the 
inducing ? 

(3) Tell how you would determine the presence and 
nature of a charge by the use of a gold-leaf electroscope. 

Experiment 41 

The Pith-ball Electroscope and its Use. 

Apparatus. — A glass rod ; a rubber rod ; a silk and a flannel pad ; 
a ball of corn or sunflower pith suspended by a silk thread. 

(1) Suspend the pith ball from a convenient support, 
and bring a charged rod near it. What is the first action ? 
What follows this ? After the pith ball has touched the 
rod, what is the mutual action between the two ? 

At first the ball was neutral ; after touching tlie rod 
you would expect it to have what kind of a charge ? 
What have you found to be the action of like charges 
upon each other ? Touch the pith ball with the fingers, 
and see if it will be again attracted by the rod. Touching 
it discharges it. 

(2) Bring a charged glass rod up under the ball, and, 
while holding it about two inches from the ball, touch the 



VOLTAIC ELECTRICITY 35 

ball with the fingers; then remove first the fingers and 
then the rod. Again bring the glass rod near, but not so 
that the ball can touch it. Is it attracted or repelled ? 
Bring a charged rubber rod near. What is its action? 
What must have been the charge upon the ball ? 

(3) The first method of charging was by contact or 
conduction and the last by induction, and the rod is called 
the charging or inducing body. How do the inducing and 
induced charges compare ? Tell how you can determine 
the nature of an unknown charge. 

VOLTAIC ELECTRICITY 

Experiment 42 
The Simple Voltaic Cell. 

Apparatus. — A tumbler nearly full of 10 per cent sulphuric acid ; 
strips of copper and zinc ; pieces of insulated copper wire ; a wire 
connector ; a compass ; a piece of board 1x^x3 in., with two slits 
sawed two-thirds of its length about | in. apart (Fig. 23). 

Solder one end of a piece of copper wire to each of the 
copper and zinc strips, leaving the other ends of the wires 
free. 

(1) Place a copper and a zinc strip / ^ 

in the slits in the board, and allow j/- 

them to hang in the dilute acid, but -p^^ 23 

do not allow the strips or the wires 

attached to them to touch each other. Note any action 

which takes place. The gathering of gas bubbles upon 

either of the plates indicates chemical action. 

Connect the free ends of the wires with a wire con- 
nector, and again place the strips into the acid. Do you 
note any difference in the conditions in the cell ? These 
strips are called elements or a voltaic pair. The acid is 
called the exciting fiuid. 



36 LABORATORY MANUAL 

Place the compass on the table, and holding the con- 
necting wire from the elements in a north and south 
direction, bring it down over the compass needle while the 
elements are out of the acid. Do you get any results ? 

Place the elements in the fluid and repeat. Result ? 
Is there any evidence of a force in or around the wire that 
was not there before ? This condition in or around a con- 
ductor is called a voltaic current. 

The chemical action takes place upon the zinc plate, 
and for convenience the zinc plate is called the positive or 
+ plate, and the copper plate the negative or — plate. 
The current is said to flow from the zinc to the copper in 
the fluid, and from the copper to the zinc in the external 
circuit. The end of the wire attached to the copper plate 
is called the -|- electrode, and that attached to the zinc 
plate the — electrode ; so the current flow is always from 
+ to -. 

(2) Scrape or sandpaper one of the zinc strips, and 
amalgamate it by dipping it in a prepared amalgamating 
fluid, or by dipping in acid and then rubbing with a little 
mercury. Use this in place of the zinc first used. Do 
you notice any difference in the action of this pair either 
when the wires are connected or disconnected ? 

Experiment 43 

To study the Relations between the Direction, Position, 
and Strength of Current and the Direction and Amount of 
Deflection of a Compass Needle. 

Apparatus. — A tumbler or other cell ; a compass ; a meter or more 
of connecting wire. 

(1) Connect the ends of the wires attached to the ele- 
ments as in Experiment 42. Place the elements in the 
fluid, and remembering what was learned in Experiment 



VOLTAIC ELECTRICITY 37 

42 about the direction of the flow, hold the connecting 
wire so that the current flows from north to south, and 
bring the wire down over the needle. 

Which way is the north pole of the compass deflected? 

Lay the wire down with the current flowing in the same 
direction and set the compass upon it. Result? Now 
change the wire so that the flow is from south to north, 
and repeat. Record all results in a table recording the 
direction of flow and direction of deflection of the north 
pole of the needle in each case. 

(2) Wrap the wire once around the compass so that the 
wire passes over and under the needle, and, holding the 
coil thus formed in a north and south direction, place 
the elements in the fluid. How does the amount of deflec- 
tion compare with that obtained before? Now wind it 
several times around. Result? 

(3) Connect the two cells as shown in Fig. 24 so that 
the two copper and the two zinc plates are connected to 
the same wire, and repeat (1) and (2). How 
does the amount of deflection in this case com- 
pare with the first? What do you find affects 
the amount of deflection? 

(4) Place the right-hand palm toward the 
needle as if it were floating in the current with 
the fingers pointing in the direction of the flow, 
and it will be found that the thumb is always 
on the side of the deflection of the north pole ; or, con- 
versely, if the direction of the current is not known, place 
the hand as directed with the thumb on the side of the 
deflection of the north pole and the fingers will point in 
the direction of the flow of current. 

This is a common method used by electricians for deter- 
mining the direction of flow when connections are made 
with unknown poles. 




38 



LABORATORY MANUAL 



Experiment 44 




Resistance and its Effects. 

Apparatus. — A good cell ; coils of Nos. 24 and 28 copper wire, 50 
and 100 ft. long, and a 50-ft. coil of No. 24 German-silver wire; a 
commutator or current reverser (R, Fig. 26) ; a tangent galvanometer. 

A tangent galvanometer 
is simply a circular rim of 
wood with insulated copper 
wire wound around its rim 
and a magnetic needle piv- 
oted in the center (Fig. 25). 
When a current is passed 
through the coil of wire the 
needle is deflected and the 
amount of deflection is deter- 
mined by the strength of the 
current. 

(1) Arrange the apparatus 
as shown in Fig. 26 so that the current flows directly to 
the galvanometer, and note the deflection of 
the needle. 

The coil of the galvanometer should be set 
in a north and south direction, so that when 
the needle is at rest with no current it will be 
parallel to the coil. 

Reverse the current through the galva- 
nometer by turning the reverser contacts one- 
fourth of a circumference, and again take 
the compass reading. The average of these 
two readings will be the correct reading of the galva- 
nometer. 

Place the 50-ft. coil of No. 24 copper wire in the cir- 
cuit so that the current must flow through it, as shown in 



Fig. 25. 




Fig. 26. 



VOLTAIC ELECTBICITY 



39 




Coil 



Fig. 27. 



Fig. 27, and again take two readings as before. What 
do you find as to the amount of deflection 
compared with the first? 

(2) Replace this coil with the 100-ft. 
coil and repeat. Repeat with the two coils 
of No. 28 copper wire and the German-silver 
wire. 

(8) Make a table of results showing the 
kind of wire, size, length, and average 
deflection of the needle in each case. 

(4) What is the effect of resistance upon the flow? 
What is the effect of increased length of a conductor upon 
its resistance ? How does the size or diameter of the con- 
ductor affect its resistance ? Does material affect the re- 
sistance of a conductor? State your conclusions in the 
form of laws. 

Experiment 45 

Measurement of Resistance by Substitution. 

Apparatus. — A good cell ; a tangent galvanometer ; a reverser ; a 
resistance box ; a coil of wire to be measured ; a contact key. 

Connect the apparatus as shown in Fig. 
28, so that the current must flow through 
the coil, the resistance of 
which is to be measured. 
The key jfiTshould be placed 
in the circuit to make and 
break the circuit. Com- 
plete the circuit and take 
the reading of the galva- 
nometer. Reverse and re- 
peat, and get the average reading. 

Now substitute the resistance box RB 
for the coil, as shown in Fig. 29. A fig. 29. 





40 LABORATORY MANUAL 

resistance box is a series of coils of wire which are con- 
nected by switches or plugs, so that any resistance from 
.1 ohm to 100 ohms, or more, may be obtained. Remove 
plugs until the reading of G- is the same as when the coil 
was connected, then the resistance of MB will be the same 
as the coil, for there will be the same flow of current. 



ELECTROMAGNETS 

Experiment 46 

Study of the Electromagnet. 

Apparatus. — A round bar of soft iron, ^ or | x 3 in. ; 6 or 8 ft. 
of insulated copper wire ; a contact key ; a reverser ; if convenient, a 
cell used in Experiment 42 ; a 100-f t. coil of l^o. 28 copper wire ; a 
compass ; some iron filings. 

(1) Test the iron bar for magnetism, and then wind 
about twenty turns of the wire around it and connect it 
in the circuit of the cell, as shown in 
Fig. 30. Complete the circuit and again 
test the bar for magnetism. Also test 
it by seeing how many iron filings it will 
pick up. 

Test the two ends for polarity by 
bringing it near the compass. 

Reverse the current and see what effect 
it has upon the poles. 

(2) Double the number of turns of 
Avire around the bar and again test for 
strength. Place the spool of No. 28 wire in series with 
the magnet. This will decrease the flow of current. See 
what effect it has on the magnet. The bar of iron is 
called the core, and the coil of wire surrounding it is 
called the helix. 




ELECTROMAGNETIC INDUCTION 41 

(3) Complete the circuit and place one pole of the .core 
in the iron filings, and see how many it will pick up. 
Break the circuit. Result ? 

(4) Grasp the magnet in your right hand with the 
fingers pointing in the direction of the flow of current, 
and see which pole is indicated by the thumb. Reverse 
the current and repeat. Does the thumb always point 
toward the same pole ? 

Sum up fully those things which determine the strength 
of an electromagnet and the direction of its poles. 



electromagnetic induction 

Experiment 47 
Induced Currents. 

Apparatus. — A large coil of small insulated copper wire,'with a 
iiole in the center of the coil not less than 1 in. in diameter ; a bar 
magnet ; an electromagnet that will go into the hole in the larger coil ; 
a sensitive galvanometer; a cell; a contact key. 

(1) Place the galvanometer at one end of the table and 
the large helix at the other, and connect the terminals 
of the helix to the binding-posts of the galvanometer. 
Thrust the north pole of the magnet quickly into the helix, 
and note the effect upon the galvanometer. Withdraw the 
magnet and again note the effect upon (r, both for amount 
and direction of deflection. Reverse the magnet and re- 
peat. Result ? How do the currents sent through the 
galvanometer as the magnet goes in and comes out com- 
pare as to direction ? as to strength ? 

(2) Now connect the apparatus as in Fig. 31, connecting 
the electromagnet with the cell through the key, and placing 
it in the large helix. The inner coil is called the primary 
and the outer one the secondary. Make the primary cir- 



42 



LABORATORY MANUAL 



cuit by depressing the key while watching (7. Result ? 

Break the primary 
circuit. Result ? 

In which case do 
you get the stronger 
secondary or induced 
current ? How does 
making and breaking 
the primary circuit 
compare with thrust- 
V ing in and withdraw- 

ing the magnet ? 
These secondary 
currents are formed by the cutting of the lines of mag- 
netic force by the turns of wire forming the secondary 
coil. The induction or Ruhmkorff coil is simply a primary 
and secondary coil in which the primary current is auto- 
matically made and broken. This rapidly magnetizes and 
demagnetizes the core of the primary, and induces currents 
in the secondary coil. 




SOUND 



Experiment 48 



Motion of Sonorous Bodies. 

Apparatus. — A tuning fork ; a bell ; a thread ; a piece of cork. 

(1) Sound a tuning fork, and hold one of the prongs 
against the cheek. 

Sound the fork again, and dip the prongs slightly into 
water. 

(2) Strike a bell, and hold against its edge a piece of 
cork or pith suspended from a thread. If the bell does 
not cause the cork to vibrate, strike the bell again and 



SOUND 43 

move the cork along a little. Some portions of the edge 
of the bell vibrate while other portions do not. 

Draw some conclusion from the results of the experi- 
ment. 

Experiment 49 

Intensity of Sound. 
Apparatus. — A tuning fork. 

(1) Strike a tuning fork and notice the intensity of 
the sound. 

Strike it again so that the intensity will be about the 
same as before, and hold the handle of the fork against 
the top of a table, or against a door or window-pane. 

Strike the fork harder one time than another, and 
notice the increased sound. 

(2) Place the ear against a door while another student 
holds one end of a long wooden rod against the other side 
of the door and at the same time holds a sounding tuning 
fork against the other end of the rod. 

Draw conclusions in reference to the effect of area and 
amplitude of vibration of sounding bodies, and of media, 
on the intensity of sound. 

Experiment 50 
Pitch of Sound. 

Apparatus. — A vise ; a flat steel band ; a comb ; a piece of card- 
board. 

(1) Clamp in the vise, or to the table top with an iron 
clamp, one end of the steel band or a thin strip of hard 
wood. Pull the projecting end to one side and release it. 
If the vibrations are too slow to cause sound, shorten the 
projecting portion and repeat. 

Shorten again and repeat, and notice that as the portion 
becomes shorter the frequency increases and the pitch of 
the sound produced rises. 



-Q — Q — Qt — Qr 



^ 



Fig. 32. 



44 LABORATORY MANUAL 

(2) Rub the edge of a piece of cardboard along the 
teeth of a comb. Repeat more quickly, and notice the 
increase in pitch. 

Experiment 51 

Effect of Tension on Frequency. 

Apparatus. — A sonometer with a wire the tension of which may be 
increased readily. Several small weights of equal mass, — small brass 
or iron nuts will do ; some rubber bands. 

(1) Stretch the wire on the sonometer, or any sound- 
ing board, and notice its pitch. Increase the tension of the 

wire, and again notice its pitch. 

(2) Connect a number of the 

weights by rubber bands, and 

suspend them as indicated in 

Fig. 32. Cause the string of 

weights to vibrate. 

Secure shorter bands and suspend the same weights, 

stretching the bands so that the total length will be the 

same as before. Cause the weights to vibrate again. 

Repeat with still shorter bands, if possible, stretching the 
string of weights to the same length as before. 

Draw a conclusion as to the effect of tension on 
frequency. 

Experiment 52 

Effect of Mass on Frequency. 

Apparatus. — A sonometer with two wires of unequal masses, but 
equal lengths; some weights similar to those used in Experiment 51> 
and some heavier weights. 

Stretch the two wires on the sonometer, and secure 
equal tensions by passing one end of each wire over a 
pulley and suspending on the ends equal weights. Pluck 
the wires, and from the relative pitches determine the 
relative frequencies. 



SOUND 45 

Stretch two strings of weights as in Experiment 51, one 
with the light weights and one with the heavy weights, 
using care to have the tensions equal. Cause them to 
vibrate simultaneously, and notice their relative fre- 
quencies. 

Experiment 53 
Sounding Boards. 
Apparatus. — A sonometer ; a stout wire ; a weight of about 20 lb. 

Suspend the wire from a heavy beam or rigid support. 
At the lower end of the wire suspend the weight. Pluck 
the wire, and notice the intensity of the sound. 

Fasten the string about an inch above and parallel to 
the top of a table or desk, and stretch it by means of the 
same weight. The ends may pass over the edges of the 
table, without pulleys, with equal weights suspended from 
them. Pluck, and notice the intensity again. 

Stretch the wire on the sonometer with the same ten- 
sion, and again notice the intensity when plucked. 

Draw a conclusion as to the need of sounding boards. 

Experiment 54 
Beats. 

Apparatus. — A glass tube of about 6 mm. bore and 15 cm. long; 
two large glass tubes, each about 3 cm. in diameter and 70 cm. long, 
one being slightly longer than the other ; two rubber tubes connected 
to the gas supply pipe. 

Heat the small tube at the center until soft and draw it 
out so that the bore will be not over 1 mm. When cold, 
scratch with a file at the smallest place, and break in two. 
Pass the free ends of the rubber tubes over the large ends 
of the tubes, and support them vertically about a foot 
apart. Turn on the gas and light, and turn it down until 
the jets are an inch or so in length. 



46 LABORATORY MANUAL 

Pass one of the large tubes down over one jet, and shift 
it slowly up and down until a loud note is heard. Pass 
the other tube over the other jet in the same way. 

When both are sounding loudly, if beats are not heard, 
shift them slightly, one up and the other down, until the 
beats are distinct. 

LIGHT 

Experiment 55 

Umbra and Penumbra. 

Apparatus. — An illuminating burner; a cardboard screen; a dark 
room. 

(1) Hold the cardboard between the gas jet, turned 
flatwise, and a white screen, and notice the difference in 
intensity of the shadow on the screen at different places. 

Near the outer edge of the shadoAV, where it is less 
intense, punch a hole through the screen, and, by looking 
through the hole, notice whether all of the light from the 
jet falls" on that part of the screen. 

Punch a hole in the in tensest portion of the shadow and 
notice how much light falls there. 

The part of the shadow where no light falls is called the 
umbra^ and the remainder is called the penumbra. 

(2) Turn the jet low so that it approaches a point of 
light, and notice the change in the amount of partly illu- 
minated portion, or the penumbra. Turn the jet edgewise 
when it is turned high, and notice the penumbra on the 
sides of the shadow. 

Experiment 5Q 

Effect of Distance on Illumination. 

Apparatus. — A piece of cardboard about 20 cm. square, with an 
opening of about 1 cm^. cut in its central portion. Five candles with 
holders ; a darkened room. 



LIGHT 47 

Put a piece of thin unsized paper over the opening in 
the cardboard, and, holding the cardboard horizontal, place 
on the unsized paper a small piece of paraffin ; heat the 
paraffin over a burner until it soaks thoroughly into the 
paper. This screen is called a Bunsen photometer. 

Support the screen vertically, and place four lighted 
candles in a row on one side and the other candle lighted 
on the other side, keeping the jets, by proper trimming, 
as nearly of the same size and brightness as possible. 

Screen off all outside lights, as well as light from the 
candles reflected from the walls or surrounding objects. 
The screens should be of black wool, if possible, as that 
will reflect no light. 

Move the cardboard screen toward the one light or the 
four until the paraffin spot appears of equal brightness on 
the two sides. Then measure the distance from the screen 
to the two sources of light. 

Remove the screen and replace it several times, taking 
measurements each time, until practice produces accurate 
results. 

Square the distances found and determine the effect of 
distance on illumination, bearing in mind that the intensi- 
ties of the lights are in the ratio of one to four, and that 
the illumination is the same from the two sources. It is 
also well to remember in all such experiments, that with 
the apparatus used and the inexperience of the student, 
it is hardly possible to obtain exact results. All that can 
be done is to draw conclusions that are approximately 
supported by the experiment. 

Experiment 57 

Candle Power of Light. 

Apparatus. — The Bunsen photometer used in Experiment 56 ; a 
light, the intensity of which is to be determined; a standard candle. 



48 LABORATORY MANUAL 

Place the photometer between the light and the lighted 
candle. Shift it until equal illumination is obtained on 
both sides of the paraffin spot, and measure the distance 
from the screen to each light. Repeat several times, with 
the lights at different distances. 

Assuming that the intensity of illumination varies in- 
versely as the square of the distance from the source of 
light, determine the candle power of the light. 

Experiment 58 

Angles of Incidence and Reflection. 

Apparatus. — A plane mirror ; a pair of calipers; a try-square. 

Allow a beam of sunlight to pass through the shutter 
or curtain of a darkened room. Or better, throw a beam 
into the room with an optical lantern. Allow the beam to 
be reflected by the mirror, and open the calipers until the 
angle formed by its arms is equal to the angle formed by 
the mirror and the incident beam. If the beam does not 
show clearly, strike the chalk from a blackboard eraser so 
as to increase the number of dust particles in the path of 
the beam. 

Test with the calipers whether the angle between the 
mirror and the incident beam is equal to that between 
the mirror and the reflected beam. 

With the try-square, find whether the plane formed by the 
two beams is approximately perpendicular to the mirror. 

Tip the mirror at different angles and repeat both tests. 

The angles of incidence and of reflection are the angles 
formed by the incident and the reflected rays with the 
perpendicular to the surface. Draw a conclusion as to 
the relation between these angles in case of reflected 
light. What angle does the plane passing through these 
angles form with the mirror ? 



LIGHT 49 

Experiment 59 

Location of Image with Plane Mirrors. 

Apparatus. — A plane mirror ; a ruler. 

(1) Look at the image of some object in a plane mirror. 
Leaving the mirror and the object at rest, move the eye 
in various directions and notice whether the image and 
mirror seem to change their relative positions. If not, 
evidently the location of the image depends only on the 
location of the object and the mirror. 

(2) Place the end of the ruler against the mirror, and 
hold the ruler normal to the surface. Notice whether the 
ruler and its image form a straight line. If so, a straight 
line joining the object and image must be perpendicular to 
the surface. 

(3) Notice whether the divisions on the ruler and on the 
image appear equal in length, or whether the image of the 
ruler is the same length apparently as the ruler itself, and 
draw a conclusion as to the relative distances of the object 
and the image from the surface. 

Formulate a law in reference to the relative positions of 
objects and their images with plane mirrors. 

Experiment 60 
Images with Concave Mirrors. 

Apparatus. — A concave mhror ; a cardboard screen about 20 cm. 
square. 

(1) Allow sunlight to fall upon the mirror, and cast an 
image of the sun on the screen held in front of tiie mirror. 
Move the screen until the image is as small and bright as 
possible. The image is then at the principal focus of the 
mirror, or it would be if it were directly in front of the 
mirror. 



50 LABORATORY MANUAL 

Measure the distance from the image to the center of the 
mirror. This distance is called the principal focal distance. 

(2) In a darkened room place a light about twice the 
principal focal distance from the mirror. Hold a screen 
opposite to the light so that a line perpendicular to the 
center of the mirror would pass between the screen and the 
light. Move the screen and light slightly, if necessary, 
until a distinct image of the light is cast upon the screen. 
The point midway between the image and the light is then 
the center of curvature of the mirror. 

Measure the distance from this point to the mirror. 
This is the radius of curvature. 

What relation seems to hold, at least approximately, 
between the principal focal distance and the radius of 
curvature ? Repeat the last test with the light as small 
as possible, and compare the two distances again. 

(3) Move the light farther away from the mirror, and 
shift the screen nearer until an image is again formed. 
Interchange the screen and the light with reference to their 
positions. If an image is again formed, the image' and 
object are in conjugate foci. 

Experiment 61 

Real and Virtual Images. 
Apparatus. — A concave mirror. 

In Experiment 60 in each case the image was thrown 
upon a screen, and necessarily the rays of light actually 
passed from the flame to the image, as that portion of the 
screen was illuminated more than the rest. Hence the 
images were real ; they actually existed. 

Place the light between the principal focus and the 
mirror, and it will be found that an image can no longer 
be thrown on the screen no matter Avhere it is placed. 



LIGHT 



51 



There will be a blur of light on the screen, necessarily, as 
the rays must be reflected backward; but there will be 
no distinct image formed. 

The eye, however, can still see the image of the light in 
the mirror. So an image results, but it is virtual. 



Experiment 62 
Refraction. 

Apparatus. — A piece of plate glass, about 8 cm. square, with two 
opposite edges parallel and polished. Some pins. 

(1) Draw a line across 
a sheet of paper, and place 
one edge of the glass on 
the line. Stick a pin into 
the table top at the point 
A (Fig. 33). Place an- 
other pin at the point B. 
Hold the eye just above 
the table top, and notice 
the images of the pins 
through the glass. Shift 
the eye until the two images arc in the same line. Place 
two pins a few inches apart in line with the two images, 
at the points and D. Use much care in getting these 
images and pins all exactly in line. 

Remove the glass and draw the line 
ABE, BO, and CD. Then ABCB repre- 
sents the path of the light as it passed 
from the pin at A to the eye. 

How is the light affected when it 
___^__^ passes through a denser medium with 

y J parallel surfaces? 
^^^ (2) At B and C (Fig. 33) draw the per- 

pendiculars Bv and Cfe, as shown in Fig. 34. 





52 LABORATORY MANUAL 

When light passes into a denser medium, is it refracted 
toward or away from the perpendicular to the surface? 
How is it when it passes into a rarer medium ? 

(3) With C (Fig. 34) as a center, draw a circle with 
any convenient radius, and draw the lines, Cw, wx, and 
1/z. Then yz divided by wx is the index of refraction of 
the glass with reference to air. 

Experiment 63 

Images with Convex Lens. 

Apparatus. — A double convex lens of about 10 cm. focal length; 
an illuminating burner or candle ; a darkened room. 

(1) Allow the sunlight to fall upon the lens, and cast 
an image of the sun on any convenient screen. Shift the 
screen until the image is as small and bright as possible. 
The image is then at the principal focus of the lens. 

Measure the distance from the image to the center of 
the lens. This distance is the principal focal distance. 

(2) In the darkened room place the lens midway between 
the light and the screen, with the screen and the light 
about four times the principal focal distance apart. Shift 
the lens and the screen until a distinct image is formed 
while the lens is midway between the light and the screen. 
The light and its image are then at the secondary foci 
of the lens. 

Measure the distance between the light and its image. 
This distance would be four times the principal focal 
distance if the light were a point. 

(3) Hold the screen farther from the lens than twice the 
principal focal distance, and bring the light nearer until a 
distinct image is formed. Then change the positions of 
the light and screen. If an image is again formed on the 
screen, the light and its image are in conjugate foci. 



LIGHT 53 

Experiment 64 

Real and Virtual Images with a Lens. 

Apparatus. — A double convex lens ; a screen ; an illuminating 
burner or candle. 

In Experiment 63 the images were all thrown on a 
screen, and they were therefore real. 

Move the light from near the secondary focus slowly 
toward the lens, at the same time moving the screen so 
as to keep upon it an image of the light. When the light 
reaches the principal focus the image will become some- 
what blurred. If it were then a mere point the light on 
the screen would be a circle about the size of the lens. 

Move the light still nearer the lens and the image will 
become more blurred and enlarged and will finally dis- 
appear. If, now, the light through the lens is allowed 
to fall upon the eye, an image of the light will be seen. 
This image is virtual. 



A Laboratory flanual 

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ARRANGED AND EDITED BY 

EDWARD L. NICHOLS, 

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